If you think about it, the most obvious thing a team on offense can do to move the ball down the field is to have the "snapper" (actually commonly called the "center") snap the ball to a teammate who simply runs towards the goal, with teammates blocking a path for him/her. A play without a forward pass is simply called a "running play".

I say it's the most obvious thing to do because:

Power; Speed; Deception

There are essentially three elements in American football to successfully advancing the ball down the field: power, speed, and deception.

Pretty much everything you see in a football game is about what teams can do with these three elements.

"When the field gets muddy in baseball, they stop the game. When the field gets muddy in football, the players roll in it like boar hogs"
-Ira Berkow, sportswriter

Touchdown (6 points):

If a team is successful in moving the ball all the way down the field and they move the ball past the end of the field, into the "end zone", (the goal area), they score a touchdown, which is worth 6 points. A touchdown can be scored either by having a ball-carrier run into the end zone, or, by having a player catch a pass while in the end zone.

"When in doubt, punt."
-Knute Rockne, famous football coach and player

A punt is a kick which, unlike a field goal, does not touch the ground before it's kicked, and cannot score any points. It's a strategic tool meant to force the other team back deep into their own territory.

In American football the team with the ball -- the offense -- is given four plays to advance the ball a minimum of ten yards. If the offense cannot advance the ball at least ten yards in four attempts, the other team gets the ball.

"Baseball is easy to fathom, not like football, which people explain to me at great length and I understand for one brief moment before it all falls apart in my brain and looks like an ominous calculus problem."
-Eve Babitz, writer

Fair enough.. I'll try to be simple.

In football, the team with the ball will try to score and the other team (without the ball) tries to stop them.

"Lord, don't ever phone me the day after a game. I'll either be still getting drunk or lookin' for bail. When you're on a suicide team like I am, you don't wait till next week to start living."
-Mike Battle, New York Jets kick returner

"You've heard about the Rubber Band Defense that bends but never breaks? Ours doesn't break either, but it streches 101 yards."
-Don Smith, New York Giants publicist, 1971

"Football is a game designed to keep coal miners off the street"
-Jimmy Breslin, Columnist

The American version of football has been played in some form or another for a very long time, perhaps for hundreds of years. Like soccer and rugby and baseball it was first officially organized in the nineteenth century. In its present form American football is essentially based on the English game of rugby.

"A game that can keep you young and vibrant and all steamed up is a precious thing"
-W.W. "Pudge" Heffelfinger, Yale lineman, (and first ever pro player)