In the novel The Outsiders, Greasers may not have much, but they have a "rep." Why is their "rep" considered something?

In the aptly named novel, The Outsiders, Ponyboy points out, in chapter one, that the Greasers are the local gang of boys from "the East side." They know that they are frowned upon in their local community, unlike their rivals, the Socs. Socs are "the jet set" and are a "public disgrace one day and an asset to society the next."

Ponyboy's impression of the way things are exposes the inconsistencies in the system,...

In the aptly named novel, The Outsiders, Ponyboy points out, in chapter one, that the Greasers are the local gang of boys from "the East side." They know that they are frowned upon in their local community, unlike their rivals, the Socs. Socs are "the jet set" and are a "public disgrace one day and an asset to society the next."

Ponyboy's impression of the way things are exposes the inconsistencies in the system, and makes it easier to understand why he and Johnny run when Johnny kills a Soc in self-defense. Ponyboy believes that a Soc would be believed over a Greaser any day. This is why the Greasers' reputation ("rep") is so important to them. Even though they have to function on the periphery of their community, they do have a place in it, and among their peers, are easily recognizable by their appearance, and their tough as nails attitude. 

Ponyboy and Johnny have to hide out, but become the center of attention after saving some children from a burning church. In chapter six, when it is suggested that the boys were "sent from heaven," Ponyboy is confused because he thinks it must be quite apparent that, "we're Greasers," so that comment does not make sense to him. 

In chapter nine, the boys are preparing for the "rumble" that will take place later in order to even the score between the Greasers and the Socs. While they grease their long hair, of which they are so proud, Ponyboy considers "What kind of world is it where all I have to be proud of is a reputation for being a hood, and greasy hair?" Ponyboy is far more philosophical than his friends, but wouldn’t want to be left out. The boys go on to sing a catchy tune: 

"Greaser... greaser... greaser..." Steve sing-songed. "O victim of environment, underprivileged, rotten, no-count hood!"

As distorted as this view may be, their reputation helps prevent the Greasers from losing hope. Their reputation gives them a feeling of their own community, so that they can function within a community from which they are largely ostracized.