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.
In football each attempt is called a "Down" (as most plays result in the ball carrier being "downed" or tackled). So, "first down" is the first attempt; "2nd Down" is the second attempt, etc. All teams will try to advance the ball as far down the field as they can -- they're definately not limited to ten yards on any given play -- but they must move the ball at least ten yards in four Downs or they relinquish the ball to the other team.

This ball-carrier is about to be "downed"
If a team advances the ball ten yards or more, they're given another four attempts in which to go another ten or more yards. For football teams the ultimate goal is to score points, but the main focus along the way is mostly getting first downs. Indeed, while all American sports are obsessed about statistics, American football teams are rated mostly on the amount of yardage gained, or (in the case of defenses), the amount of yardage not given up.
American football is played on a grid. It is all about territory. This seems to be the hardest part of the game for most folks to grasp.

It's important to understand that even if a team moves the ball forty yards in one single play, and they're awarded a new first down, they still have to move the ball ten yards more (within another four plays) or give the ball back to the other team.

So, while a defense can intercept a pass, or recover a fumbled ball, the normal way in American football that defenses stop offenses is by preventing new first downs. If the defense can do that their team gets the ball back.
One hundred yards is a long way to go. A typical offensive series (or "drive") may be successful in moving the ball some of that distance but most times it's eventually stopped.