If you've ever heard that expression and wondered what the heck it meant, it refers to the fact that as we get older, our gums recede. This makes more of the tooth show, and therefore look longer. It means someone is old, in other words.
Getting long in the tooth isn't just an appearance issue. It means the lower part of the tooth that should be below the gumline is exposed. This is bad for a couple of reasons: first, the part of the tooth below the gums is not as dense, with much thinner enamel than the upper part of the tooth, so it decays a lot more easily; and second, it is more sensitive, to cold, heat, or even touch.
Seeing a dentist can keep you from getting long in the tooth for a long time. Have I mentioned this fact before?