The "revenge" aspect explained... (spoilers)
Freddy's Revenge takes place 5 years after the events of the first film, and what we learn is that in that time frame, nobody has seen or had issues with Freddy stalking them in their dreams. Freddy has basically "died" in Nancy's house because the trail of teens ended. This is illustrated by the bus scene that opens the film and Freddy having to drop all the kids off aside from three who he gets to take into his hellish dream world.
Now that someone has moved into the house, Freddy begins to infiltrate Jesse's dreams, slowly at first, because he is in a weakened "ghost" state. As the film progresses, Freddy's powers increase and he begins to construct his evil plan to free himself from the house that has been holding him hostage. The more kills he gets and the more fear he gets out of Jesse fuel everything he's able to accomplish. (altering the real world through a sleepwalking dreamer) This isn't much different from part 1, as Freddy was able to manipulate the sheet in the REAL world through both Nancy and mr. "Up yours with a twirling lawnmower". It's just taken to up a few notches in part 2.
During his plan, Freddy quite enjoys what he's doing to Jesse and becoming "alive" again, so maybe he might just hang onto Jesse afterall! But when Lisa, at the pool party, is able to pull Jesse out and overpower him (Look at Freddy's face and reaction when he says "I love you Lisa"), he knows he has to get back on track and escapes out into the pool party to start spreading the fear! He kills a few people and delivers the immortal words "You are all my children now", having effectively making everyone there afraid of the " Burned Man with claws". Lisa then goes after Jesse and is able to pull out and destroy Freddy from being able to possess him anymore and all is supposed to be well, right??
But then, "the next day", Jesse is back in the dream world but this time, Freddy the bus driver has a fully loaded BUS(from the pool party event) and is picking up even more kids before he takes them back to his hellish world of nightmares! SO in a nutshell, Freddy wins and is able to get the "revenge" from being trapped in the house by Nancy and has a whole new slew of kids to torture and kill.
Who's strangling the cat?