What does this mean: to get the best of someone?

This is a bit difficult to answer, because the phrase is being used in two separate contexts. I'll start with the actual meaning of the phrase.

"to get the best of" - To outdo, overcome, or outwit

In the Snow White example, the speaker is using very clever contrast to illustrate how a polecat (skunk) outwitted its chaser. Not only did the skunk get the best of him (by outwitting him), the chaser got the worst of the skunk (the smelly spray that is a polecat's defense!).

In the song lyrics, the singer is using a more literal translation of the expression. Instead of meaning "is someone overcoming you", they are asking if someone is getting the best FROM her or the best parts of her.

Hope this helps.

Getting The Best Of You

It means to annoy them or get under their skin. People who make you do things you wouldn't normally do, out of frustration or annoyance. Like the animation would not have went way out on a limb if this polecat didn't do what he did. He got the best of him because he showed a side that he usually doesn't show

Do you mean that you meant the word "mean" in its original meaning or are you too mean to meet my mean standards? Oh, I'm going to start moaning about your mixing up all those m-words...

it means to trick them