The Arena is a place for you to build a deck, and have other people play against it. As your score increases, your arena level increases as well, meaning you get to put more points into nice perks(double/triple mark production. Double deck size, etc.).
Your score also determines the league your deck will be in. If you hover your mouse over the small question marks, it will show you waht level you need to be to have your deck be submitted into a certain league.
Your deck is also controlled partially by the Oracle. When you go to the Oracle and spin, whatever card shows up will be the card your arena deck will be forced to use. You can't make an arena deck without first spinning the Oracle.