I'm unfamilar with the word "abide" which is famously used the the movie quote "The Dude abides" (The Big Lebowski).

Looking it up in a German/English dictionary makes me believe it's "The Dude lives on", but I heard the word used on a way that makes it seem to be a variant of "approve", as in "The Dude does not abide this behavior".

I hear it used as "to obey" a lot, as in "we must all abide by the rules".

Can someone shed some light into the meaning of "The Dude abides" in the context it's been used?