Dendrochronology is more than just determining the age of a tree by counting its rings. It is also a useful tool for the study of long term climate because the width of growth rings varies with the amount of rainfall that the tree receives. A narrow ring can indicate low rainfall during a growing season while a nearby wide ring indicates abundant rain during that growing season.
Each ring consists of a band of light colored "spring wood" and a dark colored band of "summer wood". As its name implies, spring wood forms early in the growing season. It consists of large cells with thin cell walls. As the growing season winds down during the summer months, these cells become smaller and the cell walls become thicker, giving the summer wood a darker appearance than the spring wood. At the end of the growing season cell growth stops completely and the tree remains dormant until the following growing season. This transition is from one growing season to another is usually easy to see when examining the rings.
Because I normally do this activity with third grade students we don't get to involved in interpreting the rings beyond finding the age of the tree.
Different tree species naturally grow at different rates so the rings in some samples are easier to see than they are in other samples. Here are sections of trunk from three different species. These samples have been sanded smooth to make it easier to see the rings. I scanned the sections of trunk to create these images.
The first sample is a section of Green Ash (Fraxinus pennsylvanica). It measures approximately 5 inches (13 centimeters) across at its widest point. The dark mark just above and left of the center of the trunk is an old branch scar. The branch stopped growing, fell off, and was eventually hidden by new growth. Green Ash is a wetland species and typically experiences fast growth, making the rings east to see and count. The lopsided growth of the trunk may be a result of the old branch scar, less exposure to sunlight on that side of the tree, or competition from other trees on that side.
The second sample is from a Red Pine (Pinus resinosa). This sample is approximately 9 inches (24 centimeters) across at its widest and 7.75 inches (19.5 centimeters) across at its narrowest dimension. This tree was one of many planted in rows. The oval growth may have resulted from there being no competition on those sides of the trunk. I would be curious to see if other trees in this grove display similar growth patterns. Red Pine is typically an upland species. The growth rings on this sample are fairly evenly spaced and easy to see. There is a branch scar at about the 1:00 position from center halfway to the edge of the trunk. This scar did cause uneven growth for several year, but the growth eventually evened out.
For more information, including microscopic views, check out this post from November 2013.