August looks up when he hears a girl ask if she can sit across from him. She sits down, takes a bite of her unappetizing mac and cheese, and introduces herself as Summer. When one of Summer's friends invites her back to their table, she insists that their table was too crowded. Summer notes that her name matches August's, because they're both summery names.
Though Summer is doing a noble thing here by choosing to sit with August, she's also possibly damaging her friendships with her other friends by refusing to sit with them. This begins to show that there are social consequences for befriending someone that most kids don't like.
August and Summer decide that their table is the "summer table," and they go through all of their classmates to see who could sit at their table. Summer even pulls out a notebook to make a list. Some of their additions are not obviously summery—they decide Reid could sit there because his name reminds them of a reed of grass, and they think that Jack could sit there because they could use his name in a summery sentence, like "Jack will go to the beach." When they're done, Summer says seriously that they still need to let other kids sit with them even if they don't have summer-themed names, assuming they're nice.
Though the initial list-making of summery names is technically an exclusionary practice, it's telling that Summer amends their plan at the end to insist that all nice people should be able to sit with them. This reinforces that Summer is a kindhearted person and primarily judges people based on how nice they are.