Else's smile could symbolize the hope she feels of finally overcoming the stigma attached to her family. Else and Lil stand outside their society, which is even noted in the physical proximity they are granted to the girls at school:

Nudging, giggling together, the little girls pressed up close. And the only two who stayed outside the ring were the two who were always outside, the little Kelveys.

Else and Lil have learned the reality of constant exclusion and certainly have grown accustomed to the way both children and adults sneer at their clothing, the "special voice" the teacher reserves just for them, and the constant dismay over their mother's "awful" employment of being a hardworking washerwoman.

Acceptance in this town must have looked hopeless to Else and Lil. This is doubtless why Else "went through life holding on to Lil, with a piece of Lil’s skirt screwed up in her hand." The two had resigned themselves to a life of rejection and isolation, clinging only to each other.

Yet on this day, hope shined through. Kezia isn't as cruel as the other girls and has reached out to her mother before, wanting to share their treasure with everyone, including Lil and Else. And without the scornful eyes of other adults and girls around, Else was able to share in a beautiful moment of childhood, one which was wrapped in peace and a welcoming presence. The moment didn't last, but it existed.

This brief encounter surely renewed Else's hope for a world that seemed to only reject and ostracize her, and her smile symbolizes the hope that little Kezia provided.

Else Kelvey smiles at the end of the story as a result of her innocent happiness at having had the opportunity to see the beautiful doll's house and lamp. The narrator has told us that, despite the variety of families that sent their children to the village school, "the line had to be drawn somewhere. It was drawn at the Kelveys." With a washerwoman for a mother and an absent—possibly a jailbird—father, Else and her older sister, Lil, are alienated and ostracized by the other children and even, more horribly and cruelly, by their teacher. In fact, taunting Lil and Else makes the other children "wild with joy" and "deeply, deeply excited." Every other little girl gets invited to the Burnells' home to see the beautiful doll's house, and they talk about it loudly in front of the Kelveys. When the Kelveys walk past the Burnells' one afternoon, Kezia invites them to see the house, but Lil refuses at first because, she says, Kezia's "'ma told [their] ma [Kezia] wasn't to speak to [them].'" Lil knows the rules, and she knows that she and her sister are different, but Else doesn't really seem to understand yet. She only cares about seeing the house, and, when she does, she "was still as a stone." Aunt Beryl's ousting of the pair "dazed" Else, but, in the end, "Else nudged up close to her sister. But now she had forgotten the cross lady [. . .]; she smiled her rare smile." Else is still so young and so innocent that she is able to move past the humiliation she and her sister experience and simply revel in the miniature beauty of the house and its furnishings. It is enough to make her happy.

The answer is that Else, who is the younger sister of Lil, felt happy because she was able to see the famous, miniature oil lamp that was part of the decoration of the Burnell sisters' doll's house. 

The Burnells, who were socially privileged girls, received the gift of a doll's house from a house guest, as an act of gratitude toward the family. The sisters were very excited about the doll's house, but it is one of the sisters, Kezia, who notices how unique and special this lamp really is:

But what Kezia liked more than anything... was the lamp. It stood in the middle of the dining-room table, an exquisite little amber lamp with a white globe. It was even filled all ready for lighting, though, of course, you couldn't light it. But there was something inside that looked like oil, and that moved when you shook it.

The Kelvey sisters, Lil and Else, were the exact opposite of the Burnells. The Kelveys were unkempt, neglected, poor, and disliked by their peers because of their lower status. Still, Else and Lil were equally amused and excited about the possibility of seeing the doll's house, but they do not get to see it. The Kelveys were not welcome anywhere and, as such, they only knew of the doll's house through the things that the other girls said. 

It isn't until Kezia invites the Kelvey girls over, against her mother's orders, that the poor sisters are finally able to see the doll's house, and the popular lamp as well. This is significant. It means that, for the first time, and for a brief moment before the Burnell's aunt, Beryl, kicks them out, the Kelveys were extended ONE opportunity that other, happier, and luckier girls also have: that of seeing the doll's house. It is also significant because Else and Kezia, two entirely different girls from different backgrounds, are still able to appreciate the beauty and uniqueness of the lamp with the same degree of interest. This is embodied in the phrase that Else says in the end: 

I seen the lamp

She, too, had an opportunity to see and appreciate something beautiful, even if only once.