What are primal Zerg?

Primal Zergs are also referred as "original zergs". They are zerg that never left their original home planet, Zerus, and thus never evolved/mutated

Source, SC lore (and the wikis, of course!)

As for the spoiler: Kerrigan's back to her human form, retaining her boosted psyonic powers and her zerg hairs. She was mercyless in WoL but here in HoTS she moves just by pure revenge. She is dfferent than the old Queen of Blades: she probably still has a human core on her inner inside, but she's not going to be human again. So, the answer is: 99% corrupted, 1% still Sarah.

BIG BIG BIG SPOILER (not really, you can find it in the wiki):

In the final scene, the camera pans around space and galaxy while Kerrigan narrates, stating that she must face her true enemy after renouncing everything she has and embraces her role as the leader of the Swarm.

The primal zergs are the zergs that did not get corrupted by Amon (or whatever how we write the name of Dark Voice).

They are the original zergs that were made by the Xel Naga. The zergs we know that can be part of the Swarm were corrupted to be made into weapons. All the zergs in the swarm share a psyonic link with each others and that makes them dependent on their leader. A leaderless brood isn't more dangerous than wild animals (as can be seen in Flashpoint or the second book of the dark templar saga).

The primal zergs don't have that psychic link. Packs are made like wolf packs where there is an Alpha male (Brack in the Zeras mission is one of the alpha). From what I can see in the mission, most current Zerg units seems to have evolved from the primal zergs in some way. The primal zergs are also independent and only respect power. Also, each primal zerg have the ability to indivually evolve by absorbing essence while the swarm has to go through more steps to evolve.

tldr; They are the original zergs. Most zerg units have evolved from their primal zerg counsins.