What's Up With the Title?
Dude, we spent the entire movie wondering that as well, no joke.
Well, no, let's back up: we spent the entire movie worried that the Half-Blood Prince was Voldemort.
Think about it. The student who originally owned Harry's potions book—the guy who called himself the "Half-Blood Prince"—was a super bright kid with a bloodline that was half Muggle and half magical. Based on a particularly nasty curse he wrote in there for use with enemies, it seems he also had an affinity for Dark magic and kind of cruel behavior.
Sound like anyone you know? Yeah, exactly. Now you get why we were a little worried Harry was taking potion recipes from Voldemort.
Turns out, though, that the Half-Blood Prince was another Slytherin that Harry despises: Severus Snape. Yup, Snape was "half-blood" as well, and as we already knew, he definitely had a taste for the dark side. And, er, apparently still might?
But hey, at least it wasn't Voldemort, right?