Wikipedia explains the method of dendrochronology, or tree ring dating:

Growth rings, also referred to as tree rings or annual rings, can be seen in a horizontal cross section cut through the trunk of a tree. Growth rings are the result of new growth in the vascular cambium, a layer of cells near the bark that is classified as a lateral meristem; this growth in diameter is known as secondary growth. Visible rings result from the change in growth speed through the seasons of the year; thus, critical for the title method, one ring generally marks the passage of one year in the life of the tree.

The rings are more visible in temperate zones, where the seasons differ more markedly. The inner portion of a growth ring is formed early in the growing season, when growth is comparatively rapid (hence the wood is less dense) and is known as “early wood” (or “spring wood”, or “late-spring wood”); the outer portion is the “late wood” (and has sometimes been termed “summer wood”, often being produced in the summer, though sometimes in the autumn) and is denser.

Many trees in temperate zones make one growth ring each year, with the newest adjacent to the bark. Hence, for these, for the entire period of a tree’s life, a year-by-year record or ring pattern is formed that reflects the age of the tree and the climatic conditions in which the tree grew. Adequate moisture and a long growing season result in a wide ring, while a drought year may result in a very narrow one.

Direct reading of tree ring chronologies is a learned science, for several reasons. First, contrary to the single ring per year paradigm, alternating poor and favorable conditions, such as mid-summer droughts, can result in several rings forming in a given year. In addition, particular tree species may present “missing rings”, and this influences the selection of trees for study of long time spans. For instance, missing rings are rare in oak and elm trees.
Critical to the science, trees from the same region tend to develop the same patterns of ring widths for a given period of historical study. These patterns can be compared and matched ring for ring with trees growing at the same time, in the same geographical zone (and therefore under similar climatic conditions). When these tree-ring patterns are carried back, from tree to tree in the same locale, in overlapping fashion, chronologies can be built up—both for entire geographical regions and sub-regions. Moreover, wood from ancient structures with known chronologies can be matched to the tree ring data (a technique called cross-dating), and the age of the wood can thereby be determined precisely. Cross-dating was originally done by visual inspection; computers have been harnessed to do the task, applying statistical techniques to assess the matching.

To eliminate individual variations in tree-ring growth, dendrochronologists take the smoothed average of the tree-ring widths of multiple tree samples to build up a ring history, a process termed replication. A tree-ring history whose beginning and end dates are not known is called a floating chronology. It can be anchored by cross-matching a section against another chronology (tree-ring history) whose dates are known. Fully anchored chronologies extending back more than 11,000 years exist for river oak trees from South Germany (from the Main and Rhine rivers) and for pine from Northern Ireland. The consistency of these two independent dendrochronological sequences has been supported through comparison of their radiocarbon and dendrochronological ages. Another fully anchored chronology that extends back 8500 years exists for the bristlecone pine in the Southwest US.

Given the way this method of dating works, something may be dated to an exact year some thousands of years in the past. While such periods are extremely short compared to the periods of time suggested by Hutton’s analysis of geology, they may be a problem for people who believe that the book of Genesis is a literal and historical account, if they also believe that the book is inspired by God. Thus John Woodmorappe says,

A literal understanding of the biblical chronologies places the Flood no earlier than about 2,500 B.C. and the creation no earlier than about 6,000 B.C. (Allowance for unlisted names in the biblical chronologies pushes back these dates, but not much). Yet the Bristlecone Pine (hereafter BCP) long chronology, comprised of hundreds of live and dead trees, is over 8,000 years long. The presence of fossiliferous sediment under the BCPs rules out any of them being pre-Flood. So, unless we choose to push the Flood back many thousands of years, effectively disregarding biblical chronologies, how can the conflicting chronologies be reconciled? I have studied this question for many years.

First he asks whether the tree ring dating contains some kind of obvious error, and concludes that it does not:

The ring-width measurements, expressed in thousandths of a millimeter, are archived online (Graybill 1970s). What if the tree-ring series were matched incorrectly? To test this possibility, I ran the BCP series constituents through COFECHA (Woodmorappe 2003b), which is a tree-ring statistical-matching software program from the University of Arizona Tree Ring lab. The software automatically removes low-frequency variance (long-term changes in tree-ring width caused by such things as tree idiosyncrasies, tree age, breaking-through the forest canopy, etc.) and matches only the high-frequency variance (ring-to-ring changes in width), after removing autocorrelation (the tendency for a given year’s growth to be partly influenced by the weather more than one year back in time). The software measures the statistical strength of every possible matching point in two series, except the first 40 and last 40 years, which may be artifactual owing to the short length of the overlapping segments.

All of the inferred correct matches showed t-values of at least 10 to 20, and this occurring not only two tree-ring series at a time, but reciprocally for at least 10 samples per year. All alternate matches gave much lower t-values, and none reciprocally supporting each other to a sample depth greater than 3. So, unless there is something funny about the data itself, for which there is no evidence, it appears that the crossmatches are sound, and so is the BCP chronology itself.

Then he discusses the possibility of multiple rings being produced in a year, concluding that it is at least very rare for this kind of tree:

The over 8,000 years of BCP chronology presuppose that no more than one ring ever formed per year. Every so often, claims are made about bristlecone pines having multiple rings per year (Matthews 2006). The “wriggles” encountered in the BCP/C-14 progression are consistent with such a premise (Molen 2008), but there is—at present—no evidence for adult BCPs being able to produce multiple rings per growing season. While doing field work in the BCP forest (Woodmorappe 2003a), and earlier, I had the privilege of meeting many BCP specialists, some of whom had been monitoring BCP growth for nearly fifty years. They were unanimous in encountering not one BCP that ever produced more than one ring per year.

Coming to the conclusion that he cannot explain the series in this way, he proceeds to make his own proposal:

It has long been known that individual tree rings can be changed, during growth, from the climate-signal-dictated size to a different size as a result of some disturbance. This disturbance (for example, insect attack, earthquake, release of gas, etc.) can make the ring either smaller or larger. If these disturbances occurred at sufficient frequency, and reappeared in sequence in other trees at later times, the actually-contemporaneous trees would crossmatch in an age-staggered manner, thus creating an artificial chronology.

For illustrative purposes, imagine the simplified situation of only three trees, (A), (B), and (C), which started growing at exactly the same time, and each of which lived exactly 500 years. If nothing happened, the tree-ring series would normally crossmatch according to climatic signal, with the crossmatch point starting with the first ring each of Tree (A), Tree (B), and Tree (C). All the constituents of the 3-tree chronology would overlap completely, creating a chronology that spans exactly 500 years.

Now suppose that an external disturbance causes rings 2, 6, 9, 14, etc., in Tree (A) to grow much bigger or smaller than they otherwise would. At about this time, rings 1, 7, 10, 13, etc. are perturbed in Tree (B). 300 years after the disturbance of the growth of the rings in Tree (A), the sequence of disturbances repeats in Tree (B), affecting rings 302, 306, 309, 314, etc. (The repetition doesn’t have to be exact, because the discrepancy can be covered by inferred missing rings, which are common in the BCP chronology). 400 years after the disturbances in the early rings of Tree (B), similar disturbances occur in Tree (C), affecting rings 401, 407, 410, 413, etc. Identical reasoning can be applied to many more trees, and over a much longer period of time.

The net result is the fact that Trees (A), (B), and (C) will no longer crossmatch across their 500-year common growth history. They will now only crossmatch at their ring-perturbed ends. The result is an illusory chronology that is 1200 years long. Crossmatching experiments that I had performed show that it is only necessary to disturb 2–3 rings per decade, sustained across at least a few decades, in order to override the climatic signal, and to cause the tree-ring series to artificially crossmatch at the ring-perturbed ends.

He concludes,

The 8,000-year-long BCP chronology appears to be correctly crossmatched, and there is no evidence that bristlecone pines can put on more than one ring per year. The best approach for collapsing this chronology, one that takes into account the evidence from C-14 dates, is one that factors the existence of migrating ring-disturbing events. Much more must be learned about this phenomenon before this hypothesis can be developed further.

Note that, as can be seen from his examples, the “disturbances” that generally cause such changes in tree ring growth are not something that one might expect to “reappear in sequence in other trees at later times.” They are basically accidental things that will occur occasionally by chance. He does not even offer a suggestion for a process that might cause such a repeated pattern, and especially one that “takes into account the evidence from C-14 dates.”

As Gregory Dawes put it, “there is something less than serious about the spirit” in which such arguments are offered, there is “something frivolous about a philosophy of this sort.”

More plainly, it is basically obvious that Woodmorappe is wrong. The bristle cone pine chronology corresponds to 8,000 years of real tree growth, just as it appears to do. It is not some strange mystery to explain.