To overstay means to remain somewhere longer than you're welcome, expected, or allowed. When guests overstay their visit, they linger past the time when their hosts are ready for them to leave. A library book becomes overdue when you overstay the borrowing period.

The word suggests you've crossed an invisible line from welcome to inconvenient. A friend who drops by for an hour might be delightful, but if they're still there four hours later when your family wants to eat dinner, they've overstayed their welcome. Travelers who remain in a foreign country past their visa expiration have overstayed their legal permission to be there.

There's an old saying that “fish and visitors smell after three days,” which captures how even pleasant company can become tiresome if they overstay their welcome.