Late means after the expected time, or at the end of a certain period of time. if you're late for a movie, you get to the theater after the film's already started. If you're a late sleeper, you make a habit of dozing long after your alarm goes off.
When you're late, you're not on time. You might also be in your late twenties, which means you're at the end of that decade of your life — closer to 30 than to 20. If your friend calls and says, "Sorry I'm calling so late," she means late at night, at the very end of the day. And if you refer to someone as "the late Mr. Smith," it's a formal way of saying Mr. Smith is dead.