The so-called funny bone is the spot in your elbow where if you hit it, you feel a jarring, unpleasant sensation from your elbow and down into your lower arm. What you are hitting is the ulnar nerve, which passes through the elbow as it makes its way from the collar bone to the lower part of your arm.
While hitting the funny bone doesn’t usually cause any harm if it’s done occasionally and not too violently, repeated pressure on the nerve, from leaning on it on a desk, for example, can cause the nerve to be compressed and cause long-term damage.