Terry is the brother of one of the gangsters who run the dock workers' union. Terry is also kind of a moron. When he helps the gangsters get a stool pigeon onto the roof, he's actually surprised and upset when the thugs toss the poor sucker off. So, he starts dating the dead guy's sister. There's also a priest who's trying to fight against the poor working conditions at the docks. Unfortunately for him, all the guys who are willing to talk to the police are also dumb enough to put themselves where the gangsters can get at them.
This movie starts out well enough. Then it turns into mush. I realize that they wanted the film to have a message, but they wound up with too much message and not enough movie. The ending is so ridiculously optimistic that it's actually laughable. If pushing organized crime out of the unions was that easy, the gangsters would have been wiped out before the dawn of prohibition.
By the way, On the Waterfront was directed by Elia Kazan, who's most famous for accusing a number of people in Hollywood of being communists. You know, that whole Black List thing. Just a little bit of trivia for you.