Greasers dress up to maintain their image. Additionally, they do not want to be perceived as trash by the Socs. It is important to note that both the Socs and Greasers have distinctive ways of dressing and it is difficult to mistake a Greaser for a Soc or vice versa. Thus, for both groups, it is important to maintain that image and differentiation. For instance, the Greasers like to heavily oil their hair (hence the name Greasers), while the Socs dress up in expensive shirts. Although the rumble is the main event, it is important how the different groups show up, and for the Greasers, it is important to look good. Besides, their fight emanates from the issues surrounding their different social classes. The Greasers don’t like to be looked down upon because they are poor. Furthermore, neither group wants to be perceived as weak.

The greasers in S. E. Hinton's teen novel, The Outsiders, don't exactly get dressed-up--not in suits and ties or anything--but they do like to look their best when they rumble. Ponyboy was late arriving home to eat before the rumble after visiting Johnny and Dally in the hospital, and then meeting up with Cherry Valance near the vacant lot. Pony didn't have time to eat one of his favorite meals--baked chicken--but he did manage to swallow five aspirins "when Darry and Soda weren't looking" in hopes of getting rid of his headache.

    Then I hurried to take a shower and change clothes. Me and Soda and Darry always got spruced up before a rumble. And besides, we wanted to show those Socs we weren't trash, that we were just as good as they were.

The answer to this question is right there at the start of Chapter 9.

Basically, what Pony is saying is that the Greasers get dressed up for the rumble because they want to show that they are just as good as the Socs.  They do not want to look like they are just trashy little punks.

So it is a pride thing.  The Greasers want people to know that they have pride in who they are and what kind of people they are.  Because the Greasers are typically seen as the lowlifes of the community, they want to try to prove that they are not.