Also called "french Duel Commander", Duel Commander is a 1 vs. 1 variant of the Commander format. As in Commander, you have a legendary creature (your commander) at the head of a 100-card deck based around it. All the cards in the deck must have the same "color identity" as the commander and you can only play one copy of each card (except basic lands). But unlike in Commander, you only have 20 starting life. In tournaments you can also "swap" your commander after game 1 and 2 of your match, but all matches start with your pre-selected commander.
In addition to the banned cards listed below there are some cards that cannot be used as the commander, which you can find in the official banlist.