The field: A football field is 100 yards long and divided by large white markers every 10 yards; the markers start at 10 yards past each end zone and work their way up to the 50-yard line, which is in the middle of the field. The offense has to move the ball up the field to the defending team's end zone (or at least close to it) in order to have a chance to score. The team does this by continuing to make first downs in order to keep the ball in their possession.
The downs: Once you get the concept of downs, you'll be able to understand the basics of the game. The offense has four tries, or downs, to move up field by 10 yards. If they do, they get another first down and four more tries to make another 10 yards. If they don't, they must return the ball to the other team, usually by kicking it away to the other team after the third down (unless they want to take a gamble that they will get a first down on their fourth try). These days, information will appear on your TV showing you which try the team is on and how many yards they have left to move the ball 10 yards. For example, if the team runs the ball two yards, you'll see on the TV screen "second down and eight" — this means it's their second try, with eight yards left to make it to another first down.