listen (to me)聞いてくれる combines 聞く (to listen) with くれる, indicating that someone listens as a favor or for the speaker. It can also mean “will you listen?” in a casual question such as 怒らないで聞いてくれる?.
JA: ちょっと大事な話があるんだけど、聞いてくれる?
EN: I have something important to tell you—will you listen?