The Mule sends Han Pritcher to find the Second Foundation so that he can destroy it before it destroys him. They’re both tricked into thinking it’s been discovered so that the Second Foundation can, in fact, manipulate the Mule’s emotional makeup and render him harmless.
This is the worst of the Foundation stories, bar none. It has one of these elaborate back-and-forth narrative structures which Asimov occasionally experiments with (but never successfully). Asimov wanted, in fact, to end the series with this story (and it shows), but Campbell talked him out of it.