A hike in football is a backward pass from the center to the quarterback at the start of a down to put the ball into play. The center, an offensive linemen, either throws or hands the ball through his legs to the QB. It is an illegal hike to pass the ball around the side of the hip. A hike is also known as a snap. It is called a hike because the center is "hiking" the ball to start the play.
If you are not the center or quarterback during a hike, you are either trying to get open or try to stop the opposing team from getting open. This is done by either evading defenders and gunning it down the field in hopes for an open pass, or blocking the opposing team member in front of you.
The ball can either be snapped from the "under center" or "shotgun" position. The quarterback is considered under center when he is positioned directly behind the center, whereas the shotgun formation involves the quarterback being positioned approximately 5 yards back from the center. Hiking the ball from under center is much easier than hiking in the shotgun, as it requires the center to simply slide the ball back to the quarterback rather than toss it through his legs.
The quarterback is responsible for indicating to the center when the ball should be hiked. Quarterbacks notify the center in a variety of different ways, including leg lifts, clapping and verbal cadences (i.e. ready...set...HUT). It is very important that the quarterback and center are on the same page, as premature snaps can catch the quarterback off guard and result in a fumble (ball touches the ground and is up for grabs for the defense) while late snaps can result in a 5 yard penalty for not hiking the ball before the 40 second play clock expires.
The most difficult form of hiking the ball is known as long snapping. Long snapping refers to a field goal formation and requires the snapper to hike the ball anywhere from 10-15 yards back and into a kneeling player's hands to hold the ball in place for the kicker. This type of snapping is very difficult and requires a lot of practice, and it is much longer of a throw than a regular hike. This is why nearly every team has a player who exclusively long snaps during the game.