On the offensive side, there are two basic types of players: 1) linemen, who line up on the line of scrimmage and protect their teammates, and 2) ball handlers.
The five linemen consists of the "center" (in the middle of the line) who "hikes" the ball to his quarterback, two "guards" on either side, and two "tackles," who are "wide" protectors. These five linemen are not eligible to receive passes.
The six ball handlers include the quarterback, who receives the ball from the center, a big full back, who can run with the ball up the middle, a fast half back who can run with the ball to the sides, and three pass receivers, posted at the end of the line "outside" the tackles. Any of these men can receive a forward pass, and are "eligible receivers." That is, depending on the situation, the quarterback may send his halfback and fullback forward to try to catch passes instead of run with the ball.
On the defense side, there are typically four linemen (opposing five offensive linemen), and four men in the back, or "secondary, opposing the three pass receivers. Between these lines are the so-called "line backers," who are floaters that can either reinforce the lineman, if the offense is running with the ball, or the secondary, of the offense is using a pass play.
Basically, the idea was to prevent too many offensive players from doing too many different things, thereby making it too hard for the defense to counter them.