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:
The earliest example of 'what's not to like?' that I've found in print is in Dorothy Kilgallen's review of the film Charade in the 'Voice of Broadway' column in the New York newspaper The Dunkirk Evening Observer, September 1963:
"It has Audrey Hepburn, Cary Grant, Paris in living color, and a beautiful score by Henry Mancini. So what's not to like?"
The 'what's not to love?' spinoff variant started in 1974, as part of Volkswagen's advertising copy for a limited edition range of Beetle models that were styled on the Love Bug that featured in Disney's eponymous 1968 film.
It even has a picture of the said ad.
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.