Water under the bridge は、「もう済んだこと」「昔のこと」「もう過ぎたこと」という意味のイディオムです。
Water under the bridge を普通に訳すと、「橋の下の水」ですね。橋の下の水（川）は、どんどん流れて行きます。それが転じて、「もう過ぎてしまったこと」「過去のこと」という意味で使われている表現です。
Bob: Are you going to Phil’s party this weekend?
Betty: Yes, I am.
Bob: Do you want me to drive you to the party?
Betty: Are you going!? I thought that you and Phil hated each other.
Bob: Oh, that was years ago. It’s all water under the bridge now. Actually, Phil called me last week and we decided that it was stupid for us to continue being upset about something that happened twenty years ago in our college days.
Betty: Well, I’m glad to hear that you and Phil are friends again.