Position in poker refers to where a player sits in reference other players. If someone says "I've got position on you" -- it means he's sitting to your left, and will always act after you.
Most often, position is used to define where a player sits relative to the dealer and whether you'll be first or last to act in a round of betting.
Dealer Position
Your position at the table is always relative to the dealer for that hand's position. That's one of the reasons the deal rotates around the table in poker, so that everyone gets equal time in every position.
Being in the dealer position, or "on the button," is the most desirable position in poker in flop community games like Texas Hold'em, since after the flop, the person on the button will always be the last to act in each round of betting.
You can get away with playing more marginal hands on the button because of this advantage.