"Have you met him?" is asking whether you have ever in your life met this person. It's asking about the present state (right now) of whether you have ever met him (sometime in the past).

"Did you meet him?" is asking whether you met the person at a specific time. It's asking about a past state (yesterday) and is asking whether you have met him (at that point in time.)

So if I said "yesterday I was jogging in the park and saw the president." and you ask "Did you meet him?" it is asking if I met him yesterday... if you ask "Have you met him?" it is asking if I have ever met him in the past but it's not specifically asking about yesterday.

[Note: it's "him" not "he" in these questions because "him" is the object that you are meeting, not "he" which would be the subject of the sentence.]