Out of mind, out of sight (1x11) - Trance work
Early in the episode, Buffy bumps into Cordelia and drops a bundle of weapons on the floor. Cordelia and her clique mocked her for being weird and left laughing with her friends. Buffy felt terrible, still recalling the life she had in LA. She remembers when she was popular and liked, when the eyes were turned on her, and now she's an outcast, forced to live the life of the Slayer.
"I was a lot like Cordelia, minus the bullying—and I wasn't skipping meals...as much." - Buffy
Like many marginalized groups, Buffy often has to hide and reframe her slayerness or identity in a way the ingroup will understand, and that episode is no exception. That encounter with Cordelia was in large part bizarre because she had to lie about why she was carrying all those medieval weapons, or with Snyder, where she had to make up an excuse to check the crime scene, where Mitch was beated by an invisible bat.
Buffy's longing for her old life in LA intensified when Xander and Willow, lifelong friends, shown how close they are compared to Buffy, who is still new member to their circle.
"I wasn't angry at my friends, it's not their fault. I just wanted to go back to my life." - Buffy
"Can I go back to my actual life, before the Slayer stuff?" - Buffy
Buffy felt better later on, after Cordelia confessed to feeling alone, and generally not as happy as she looks even though she's popular. It reminded her of her own experience with popularity at Hemery. "It doesn't seem to matter how popular you are when..." "The point is... I did sort of felt like something was missing." - (1x11). Although she was popular and well surrounded, she did not feel necessarily alone like Cordelia, but she had a lingering sensation of something missing. She idealized Cordelia and her old self, but really Cordy has her problems and does not seem much happier than the rest, and that made her remember that her situation at Hemery wasn't perfect either.
"Is that it?" I asked myself on occasion, without really knowing what was missing. I wasn't dwelling on that sentiment all the time, but it was present in me. - Buffy
At the end of the episode, we saw a Buffy that felt comfortable with her friends, chatting and enjoying herself. Buffy had beaten Marcie, who can be understood as an extreme version of how she felt toward Cordelia or Buffy's inner demon, and through that victory she had mastered her feelings and accepted who she was. She understood that she felt better with that group of friends than back with her clique in LA. Even if sometimes she wished she could go back to being a popular girl for a day, overall she felt more complete here. It's Cordelia who came to her, this time to thank her. In her eyes, you could tell there was more than that: she saw in that group the possibility of a better life than what she has: real friendships and meaning. Her boyfriend of the time said: "You're not actually hanging out with these losers, right?" and that yanked Cordelia back to her old defenses, to her popular girl identity that she might not like but at least it's familiar territory. That little moment is the first moment where Cordelia had shown a certain character, one that will lead her in LA with Angel in a few years.
It was Willow who asked Cordelia if she wanted to have lunch, a way of asking her if she wanted to hang out with them—and Buffy was on board. She has compassion for Cordelia because she can relate to her. Buffy recognizes why Cordelia flipped them off to keep her popularity intact.
