This is a pretty vague question, but I'll give it a shot.
The basic conflict between these two groups comes from the fact that they are from very different backgrounds. The Greasers are the poor or lower middle class kids from the "wrong side of the tracks." The Socs are the rich kids with the nice cars and clothes.
The two gangs spend a fair amount of time, it would appear, trying to catch members of the other gang alone. When they do, they tend to beat them up as Johnny was beaten up and Pony was almost beaten up.
Every now and then, if there is some reason, they all get together and have a big fight (a rumble).
The Greasers and the Socs have had an on going feud with one another for a long time. The Greasers live in a poor neighborhood. They have no cars, grease their hair back, and see the Socs as having everything money can buy. They believe that the Socs have o problems because they have cars and money and can go off to college.
The Socs look down on the Greasers. They see them as the derelicts and juvenile delinquents of society. The Greasers are easy targets for the Socs because they are already labeled and more subject to be charged by the police in an incident than the Socs. They see the Greasers as having nothing, therefore they are nothing.
The conflict is one of class and social distinction and fear of not knowing one another.
The Socs pick on the Greasers because they are different. The Greasers are poorer than the Socs and they have the tendency to steal and get into gagn fights. The Greasers also like to wear their hair long and dress in blue jeans and leather jackets. The Socs on the other hand, are rich kids. They jump on Greasers and wreck houses with their drunken partying. The Greasers are ruled by the emotions while the Socs often hide their feelings behind a wall.
The Greaser's and the Soc's are from two different sides of town. The Greasers are poor and in the low class and the Soc's are rich in the upper class.
The greasers are basicly a gang that come from the poor or lower middle class neighborhood.