Ponyboy says that sunset line to Cherry in chapter 3.  Cherry is about to leave with a group of Soc boys in order to prevent a fight from breaking out in front of her. Just as she turns to leave, Ponyboy says,

"Just don't forget that some of us watch the sunset too."

His comment is meant remind Cherry that Socs and Greasers aren't so different from each other. Taking this quote out of context as just a single line, though, does the quote a disservice. The sunset concept is not first introduced to readers by Ponyboy at this point in the story. About five pages earlier, Cherry intuited that Ponyboy watched sunsets, and she admitted to watching them as well.

"I could just tell. I'll bet you watch sunsets, too." She was quiet for a minute after I nodded. "I used to watch them, too, before I got so busy . . ."

Cherry admitted this similarity to Ponyboy, and it struck him as unique and important. It's another instance when Cherry forces Ponyboy to consider the idea that Socs and Greasers are more alike than different. They both have struggles, and they both have similar loves.

I shook my head. It seemed funny to me that the sunset she saw from her patio and the one I saw from the back steps was the same one. Maybe the two different worlds we lived in weren't so different. We saw the same sunset.

This is part of what makes Cherry such a great character. She is capable of getting Ponyboy to see a bigger picture, and she first begins doing this following the flashback story in chapter 2. She tells Ponyboy that stereotyping all Socs and Greasers is not fair. More importantly, she tells Ponyboy to consider the fact that the Socs don't have it as good as it initially appears.

"I'll tell you something, Ponyboy, and it may come as a surprise. We have troubles you've never even heard of. You want to know something?" She looked me straight in the eye. "Things are rough all over."

"I believe you," I said.

Ponyboys wants to tell Cherry that they're not so different.  He may live on "the wrong side of the tracks" and she may be a rich Soc, but they're both teenagers who see the same sunset.  They live in the same town and are separated by social class, but Ponyboys wants her to know that that in itself doesn't make them totally different. 

On the way home from the movies at the Nightly Double, Pony and Cherry talk a lot and reveal things about themselves that they probably never would have imagined telling a "Soc" or a "greaser" in another situation.  They realized how much they had in common, but as soon as Bob pulled up, things had to go back to the way they'd been before.

Later in the book, Pony reminds Cherry that they both see the same sunset. 

The ability to see and marvel at the beauty in sunsets is shown to be a symbol of humanity and the capacity to live a life that is not defined by the narrow segregation of Socs and Greasers that seems to split so many young people from each other. When Cherry and Ponyboy have their conversation about sunsets, what it represents and demonstrates is that Cherry, just like Ponyboy, is human too, and they have the same joys and pleasures. The sunset motif is used throughout the novel at various stages to represent this shared humanity. Note, for example, how when Randy meets with Ponyboy before the rumble to tell him that he is not going to participate in the fight, how Ponyboy sees him as less of a Soc and more of a fellow human, as the following quote explores:

Cherry had said her friends were too cool to feel anything, and yet she could remember watching sunsets. Randy was supposed to be too cool to feel anything, and yet there was pain in his eyes.

The mention of sunsets probes the difference between appearances and reality as these young people invest so much time and energy in presenting themselves as being so hard and "too cool to feel anything," whereas actually in reality they are just the same, whether they are Socs or Greasers. The capacity to feel and be human in all its fullness is therefore symbolised in the ability to watch sunsets and enjoy them. This is why Johnny writes in his last letter that Ponyboy should tell Dally to "look at" a sunset.  

Ponyboy understands that the class separation that defines them is only a temporary situation. The young people in the separate groups (the Greasers and the Socs) use their different socioeconomic situations, neighborhoods, clothing, etc. to mock one another and convey their own superiority. When Ponyboy and Cherry become friends they begin to transcend the petty social divisions of their town. Ponyboy has a crush on Cherry, while Cherry likes Dallas (even though she is repulsed by him as well). Ponyboy suspects, perhaps, that Cherry is not as attached to her social group as she pretends to be, and seeks to reassure her that it's all right to befriend him even though they're from different groups.

In S.E. Hinton's novel The Outsiders, Ponyboy and Cherry talk about sunsets in Chapter Three. But Ponyboy doesn't remind Cherry that they both watch the sunsets, it's part of his thoughts after he talks with her. Cherry and Ponyboy talk about why their groups are so different (the Greasers and the Socs) and they come to the conclusion that it's about feelings. The Socs are cold and don't show their emotions, and the Greasers show their emotions too much. But in that conversation, they find out that they have things in common, as well. Ponyboy and Cherry both like to watch sunsets. Cherry shares that she thinks Ponyboy watches sunsets. She recognizes his sensitivity, and that's what she bases her assumption on. She also shares that she used to watch them, but then she got too busy for that. Here is the quote from Chapter Three where Ponyboy is thinking about the similarities between the Greasers and the Socs.

It seemed funny to me that the sunset she saw from her patio and, the one I saw from the back steps was the same one. Maybe the two different worlds we lived in weren't so different. We saw the same sunset.

You see here that Ponyboy is beginning to change his thinking regarding the Socs. Before, he thought they were as different from the Greasers as night and day. After the conversation with Cherry, he's thinking that they may have more in common than they previously thought.

In Chapter Three of S.E. Hinton's novel The Outsiders, Ponyboy and Cherry discover that, despite their vastly different backgrounds, and the fact that they stand respectively on opposite sides of the war between the Socs and the Greasers, they are very much alike. Both are sensitive and perceptive, and both aspire to a more intellectually rewarding future, even though Ponyboy recognizes the futility in his dreams. During their encounter, Cherry asks Ponyboy about his interest in literature, leading to her reference to sunsets:

"You read a lot, don't you, Ponyboy?" Cherry asked.

I was startled. "Yeah. Why?"

She kind of shrugged. "I could just tell. I'll bet you watch sunsets, too."

This exchange is an early indication of the rare common bond that could exist among these disparate youths if prejudices could be overcome. This is why later, in Chapter Eight, Ponyboy reminds Cherry of their emotional bond, and of the superficial prejudices that separate their worlds. The following exchange from this chapter encapsulates Ponyboy's conclusion that the Greasers are not inferior to the Socs because of their less-fortunate position on the socioeconomic ladder:

"Hey," I said suddenly, "can you see the sunset real good from the West Side?"

She blinked, startled, then smiled. "Real good."

"You can see it good from the East Side, too," I said quietly.

Ponyboy is reminding Cherry that they both watch the same sunset because he is reminding her, and himself, that they are both human beings and that neither is better than the other.