Well, counting rings is what the experts use to determine the age of trees, so I would say that it is accurate.
Closer rings means the tree didn't grow as much that year, whereas rings further apart means the tree grew quickly. This is typically due to rainfall. Years with plenty rainfall will space the rings out further. You can learn a tremendous amount about a tree and the weather in that tree's life by studying it's rings. Supposedly, you can pinpoint times when there were fires and other disasters as well. It's really pretty cool.