To let something or someone be is to leave that thing or person alone.

Dialogue

Joel: Did you hear what that guy called me? I should go and beat him in the—
Hans: He’s not worth it, mate. In the words of the Beatles, let it be … Yeah, let it be.
Joel: You’re speaking words of wisdom, Hans—I’ll let it be.

Translation
喬爾：你有聽到那傢伙剛怎麼叫我嗎？我應該去揍他……
瀚斯：兄弟，他不值得你這麼做。用披頭四的歌勸你 let it be……嗯，別理他。
喬爾：你的話有道理，瀚斯───我就不跟他計較了。

To let go of something is to stop something or someone from bothering you.

不讓某事或某人困擾你 

Dialogue

Joel: I can’t believe that I didn’t get the promotion! I just … can’t.
Hans: It’s not your fault, boy. Let it go. There’s no use in brooding over it.
Joel: Buy me a beer, and then I’ll let it go.

Translation
喬爾：我無法相信我竟然沒有獲得升遷！我……就是沒辦法啊。
瀚斯：兄弟，這不是你的錯。看開點吧。為這件事鬱卒也沒用。
喬爾：那你請我喝杯酒我就算了。