People usually say this to mean "That's not important anymore, let's forget it." It's often used to say "No worries" or "I forgive you, let's move on" - something like that. If you imagine water moving under a bridge and flowing away, it's not important anymore. So that's the comparison.

Used to refer to events or situation that are in the past and consequently no longer to be regarded as important or as a source of concern.

It means that smth has happened at one point, but you don't worry about it, have moved on, because you can't do anything about it anyway.

It's like something has already gone or done. You have over it. It's like when you fight with a friend and then you get in touch again and forget that you were sad about the fight. Things chhanged, it'a in the past, water under the bridge (like a river under the bridge, water never stops, it keeps going and going)