A lot of great answers on here. I think the main thing to remember is that it's less like a board game, and more like playing pretend.

Remember when you were a kid and pretended to be a ninja turtle or whatever and beat up the pretend bad guys? It's more like that, but the dice decide if your attempt to beat up the bad guy actually works.

The entire table works together to crate a story, and the dice rolls and the DM give you status updates on how the world reacts to the actions of your character.