At first, these two questions appear to be asking the same thing. Actually, they are asking two completely different questions.
What does he like?
Here, “like” is used as a verb. This question is asking about another person’s preferences – the food a person likes to eat, the books he likes to read, the music he likes to listen to, the TV programs or movies he likes to watch, the sports he likes to do, and so on:
- I love reading books. What do you like to do in your spare time?
- John likes spaghetti and Mary likes grilled salmon. What does Tom like?
- Christmas is coming. What toys do the kids like?
What’s he like?
Here, “like” is used as a preposition. This question is actually asking you to describe a person in some way. It is asking you about someone’s character, habits, appearance, or other unique characteristic.
- You work for Ebenezer Scrooge, don't you? What's he like? --He's an old skinflint, and refuses to spend a penny more than he has to.
- Have you met Mark? What’s he like? --He’s tall, dark and handsome.
- How was your first day of school? What’s your new teacher like? --She seems like a nice lady, but I think she’ll give us a lot of homework!
We can also use “What’s --- like?” to ask for a description of a place or thing instead of a person:
- I heard you saw the new movie. What’s it like? --It’s a spy movie, with a lot of adventure.
- Did you go to Niagara Falls on your vacation? What’s it like? --Oh, it’s amazing.