Settlement Price
  
You've heard of the closing price for a security. It's a relatively simple concept: it's the price of a security when trading finishes for the day.
A settlement price is a little more complex. Rather than just the specific price at the relatively arbitrary moment that marks the end of the trading day, the settlement price is based on the average price of a contract over the course of the session.
The concept gets used in derivatives trading (things like futures and options). The settlement price plays into calculations of profit and loss, as well as other market considerations (figuring out margin requirements, price limits for the following day, etc.).
Think of a basketball game (or any team sporting event, really). Usually, the winner is determined by the team that has the highest score at the end of a game. So...one team trails another throughout the game, but in the last few seconds, comes back and takes the lead for the first time with the final shot. The comeback kids are the winners. That's how a closing price works.
Now imagine that the winner isn't decided by the final score, but by the average score differential throughout the game. The teams have a "settlement score" at the end, instead of a closing score. Then the team that led the whole game could still come out winners in the end, even though they fell behind in just the last few seconds.