It implies that something is so funny, it would physically make someone laugh so hard they might slap themselves.
Here are some examples of how it's used:
* "That comedian was hilarious! He really slapped me silly."
* "The kids were so excited about the new puppy, it was slapping them silly."
* "The joke was so funny, it slapped me silly."
While it's an exaggeration, it expresses the intensity of laughter and amusement.