To outstay means to remain somewhere longer than you should or longer than you're welcome. When guests outstay their welcome, they linger past the point where the host wants them to leave. Maybe the party ended an hour ago but they're still chatting in the living room, or they said they'd visit for the weekend but it's now Thursday.

You can outstay your time in other situations too. A library book that you keep for three months instead of two weeks has outstayed its borrowing period. An athlete might worry about outstaying their prime, continuing to play professionally even when their skills have declined. A diplomat's assignment to a foreign country might be extended if they haven't outstayed their usefulness there.

The word carries a sense of overstaying a natural limit or boundary. There's usually a right amount of time for something, and to outstay means to push past it. It's the difference between leaving a friend's house when your parents arrive to pick you up versus ignoring three phone calls and making everyone wait. The key idea is that you've remained somewhere past the point of appropriateness, whether that's measured by social courtesy, official rules, or practical usefulness.