When a statement or a joke amuses you to a point, to an extent which would fill you with warmth and make you grin broadly, but not necessarily laugh. It gets you in a personal place. Perhaps it appeals to nostalgia, or it's simply a joke that only you find funny, or particularly resonates with you for no apparent reason.
Bob laughs at something for ten minutes.
Bill: How can you find it that funny?
Bob: No idea, it just really tickled my pickle.