If an army or an armed force overruns a place, area, or country, it succeeds in occupying it very quickly.

If you say that a place is overrun with things that you consider undesirable, you mean that there are a large number of them there.

If an event or meeting overruns by, for example, ten minutes, it continues for ten minutes longer than it was intended to.

If costs overrun, they are higher than was planned or expected.