Tree rings are layers of wood cells produced by a tree in any given year. They can be divided into earlywood - wood that grows during the late winter and spring - and latewood, which grows during the summer and fall. Latewood cells tend to be thicker than earlywood cells, as the tree stores more nutrients for survival.
Tree rings have been used for to gather an astounding amount of data about environments, cultures, and the trees themselves. For example, dendroarchaeologists measure tree rings on pieces of lumber used in ancient building sites to determine the age of the structure and the civilization that built it. Dendroecologists study tree ring widths to determine the impact of water pollution and air pollution on the trees. And dendroendochronologists may be the most interesting scientists of all: they study tree rings to track and study the migration patterns of insects in the area!
As you can imagine, it would be pretty unwieldy to chop down a tree just to measure its rings. Instead, scientists use a tool called a borer to drill a small cylinder out of the tree's side. These cylinders are usually about as thick as a finger and can be up to 5 feet long. They can use this sectional cut to measure the number of the tree rings and their individual widths and densities. Of course, it's hardly useful to merely measure the tree rings of one tree, and so scientists often pull up to 1,000 specimens in an area to do research. Fortunately, trees are very good self-medicators, and these bored holes are often covered up by bark within the year.
This writeup is indebted to Dr. Henri D. Grissino-Mayer of the University of Tennesee-Knoxville. You can visit his website (http://web.utk.edu/~grissino/) for more information.