The scrum is a means of restarting play after a stoppage which has been caused by a minor infringement of the Laws (for example, a forward pass or knock on) or the ball becoming unplayable in a ruck or maul. The scrum serves to concentrate all the forwards and the scrum halves in one place on the field, providing the opportunity for the backs to mount an attack using the space created elsewhere.
The ball is thrown into the middle of the tunnel between the two front rows, at which point the two hookers can compete for the ball, attempting to hook the ball back in the direction of their team mates. The team who throws the ball into the scrum usually retains possession, because the hooker and scrum half can synchronize their actions.
Once possession has been secured, a team can keep the ball on the ground and in the scrum and attempt to drive the opposition down field. Alternatively, they can bring the ball to the hindmost foot of the scrum, where the ball is then passed into the back line and open play resumes again.
The key player at the scrum is, of course, the scrum half. This player throws the ball into the scrum, moves to the hindmost foot of the scrum, and is usually the player who picks the ball up and passes out to the fly half who then distributes the ball to the back line. As soon as the scrum half picks the ball up, the opposition may contest for the ball and attempt to tackle whichever player is in possession. The No.8 is also an important player at the scrum, he keep the ball secure under his feet until the scrumhalf takes the ball, or he can pick the ball up and attack the (usually) open side.
Please look at the Positions page for more detailed info pertaining to the role of each player at scrum-time.
Of course it is essential that you read and understand the scrum laws!