The ending of Harry Potter and the Half-Blood Prince shows Snape killing Dumbledore, revealing Snape as the Half-Blood Prince, and sending Harry off to hunt the remaining Horcruxes. Spoilers follow.
Why does Snape do it? The film plants an answer early. Snape promises Draco's mother that he will protect her son, and when Draco cannot bring himself to kill the weakened Dumbledore, Snape arrives and kills Dumbledore instead. In my opinion, that is the cleanest reading the film itself supports: Snape acts so that Draco does not have to. It could be argued that the film leaves Snape's deeper loyalty deliberately open, and the later films, rather than this one, are where that question gets worked out.
Who is the actual Half-Blood Prince? It is Snape. The potions book that made Harry a star in Slughorn's class carried his handwritten notes, which is why the revelation lands after the death rather than before it. Harry spends the film trusting an anonymous author, and the film's last act punishes that trust.
The locket matters too. Harry and Dumbledore pay a heavy price in the sea cave, and the Horcrux they carry out turns out to be a fake left by someone with the initials R.A.B. That leaves the Horcrux hunt with nothing gained, only a name to chase.
What does Harry do next? After the funeral he decides not to return to school and to hunt the remaining Horcruxes, and Ron and Hermione promise to go with him. This sets up Harry Potter and the Deathly Hallows Part 1, which opens with Snape reporting to Voldemort and the Order moving Harry, and then Part 2.
One structural point I would make: this film ends on mourning and a decision. It is a quieter finish, and I think a deliberate one, because the film is spent mostly on memories, a potions book and a repaired cabinet rather than on set pieces.