Prosodic stress
A. They sell all kinds of toys in here. Pick something and I'll buy it for you.
B. I don't like anything round.
A. Well, what would you like then?
B. Something red.
A. Okay, something red, but what would you like?
B. I hate that bear.
A. I don't want to know what you hate. What would you like?
B. Jane likes drawing.
A. What would you like?
So the meanings break down as:
What would you like? (as opposed to some other property such as when or how you would like it)
What would you like? (as opposed to what you wouldn't or don't like)
What would you like? (as opposed to what another person would like)
What would you like? (as opposed to what you might hate, or remember, or do something other than liking with)
Such stress is about emphasis.
For all but the second one, the emphasis is to distinguish that stressed item from possible replacements. For example,
What would you like?
means that they want to emphasize that the question is about what you like rather than what you really really love or could afford or what you already have; not what you would love but what you would like.
The second sentence
What would you like?
is different in that there's really no alternative to the modal 'would' that makes sense (however one could imagine a situation where someone is talking about what one should like, and this is the alternative). But what I get out of the question is that the speaker is exasperated, the question 'What would you like?' (no emphasis) has been asked with poor responses so far.