He tells her he loves her and she believes him (she's not fifteen, of course, and instead, she believes him like the seventeen year old vampire she is) because if he didn't love her, he wouldn't say it—no one's said it to her before and no one has loved her before, so it stands to reason that because he did say it, he must really love her.

He tells her he's sorry for betraying her (and Elena and Bonnie and Matt and the whole of Mystic Falls in general) and she believes him because she's seen the switch and knows he hasn't turned it off and he loves her so she kisses his lips and tells him it'll be alright, that they'll figure it out together.

He asks her to wait for him, tells her he's on her side and that he loves her and that he's not betraying them all but that he has no choice (sired, they call it) and she says yes because she loves him back enough to believe in him even when it hurts.