I'm bored, so I'll try and give you a short rundown of the positions (I hope I don't forget any)
- Quarterback = handles the ball on almost every offensive play. Either passes to a receiver or hands off to a back
- Backs = Running backs, tailbacks, fullbacks. As far as I know, running back and tailback are the same and their primary job is to take the ball from the quarterback and run with it. The fullback's job is normally to block for the running back.
- Receivers = Lots of different names for different places on the field (split end, flanker, etc.). Their job is primarily to catch the ball but are sometimes used as blockers for the running back. Tight ends are also sometimes receivers, but they also block alongside the offensive line
- Offensive line = one of them snaps the ball to the quarterback (the center) and they all either block so that the quarterback can throw the ball or so that the running back can run effectively (they try to push the defensive players into certain spots, opening "holes" for the back to run through. I think that's it for offense...
- Defensive line = play opposite the offensive line and try to do what the offensive linemen are trying to prevent them from doing: either "sacking" the quarterback, breaking up pass plays, or tackling backs running out of the backfield. They've got all sorts of names (nose tackle, etc.), but what you see a lot is two defensive ends and two defensive tackles).
- Linebackers = Play behind the defensive linemen. Their job is to make plays, basically. The d-linemen tie up the o-linemen so the linebackers can come up through the holes and stop backs coming out of the backfield. They also drop into pass protection, most often covering backs and tight ends.
- Secondary = includes cornerbacks (line up at the line of scrimmage opposite a receiver), and safeties (strong and free, who provide deep coverage in the middle of the field and help the cornerbacks)
There's also "special teams." Outside of the other positions, these include the placekicker (kicks field goals and PATs (point after touchdown, also called an extra point) and the punter (as someone else mentioned, if it's fourth down, the team usually punts the ball so the other team doesn't get good field position and have a short distance to score). That's the punter's job.
Whew. I think that's pretty much it. I'm sure I forgot some position or got something wrong somewhere. Hope it helps, though.