To kick ass is American English meaning to dominate others. It is not appropriate for everyday use if you are not American.

‘Kick ass’ This is to defeat your opponents easily or by a large margin. Example: Roger Federer is really kicking ass this in this tournament- he’s won every match by 3 games! Incidentally - the film ‘They Live’ Starring Roddy Piper uses this phrase and is considered to be the expression of the origin.

Benjamin's explained the "kick ass" bit pretty good. Kick ass can mean beating up someone physically. It's said in a humorous fashion implying this is going to be so easy, so generally you'd only hear it used this way in a movie or TV. For instance, some "tough guy" says to his friends, "I'm going to kick ass" means he's going somewhere and he's going to easily beat up someone - at least he thinks that. In casual conversation 99% of the time it just means you're going to beat someone easily - not in a physical fight, but in a game or at some sport. It's said and taken as a joke. The sentence: "I have come here to chew bubblegum and kick ass.And I am all out of bubblegum." is a joke and a play on words. He came to chew gum and "thump" or beat someone easily at something. He's out of gum, so that leaves just one thing to do: beat someone.

I could explain, but it will be very involved. So PM me if you have to know.