This is an excellent question, and one that isn`t asked often enough. Presumably, talking about contemporary art is another one of those art definitions we are all supposed to know -- because (heaven forbid) you wouldn`t want to ask a "stupid" question at some art world function. (Well, you might, but I wouldn`t. At least, not ever again.)
Anyway, the answer is divinely simple. Contemporary just means "art that has been and continues to be created during our lifetimes." In other words, contemporary to us.
Now, of course, if you are 96-years old and reading this (By the way, congratulations, if this describes you!), you can expect a certain amount of overlapping between "Contemporary" and "Modern" art in your lifetime.