What do people really mean when they say "what's not to love"? Is there any context in particular to use this?
It's a variation on the older phrase, "what's not to like". The question is rhetorical, it's a different way of saying that you can't think of a reason why anybody would not love/like X; there is nothing not to love/like about it. At least that's what the literal meaning is. Nowadays, the phrase is such a cliché that it's often used ironically, to mean the exact opposite thing.
The Phrase Finder provides some background:
It even has a picture of the said ad.
It's a way of saying
"How can one not love ... ?"
or more precisely:
"What characteristic of ... can one dislike ?"
I think it's clearer under the form "what's not to love about ...". Such as for instance:
"What's not to love about this kid."
The confusion may arise from the elided "there".
"What's not to love?" can be expanded as "What is there not to love about [subject of discussion]?" where the italicized words are the words left out of the original construction.
The speaker is asking the listener to list objections; usually, though, the statement is rhetorical.