Players' numbers are determined by their position.

1 & 3: Props (Front Row minus hooker)
(1 is the prop loosehead, 3 is the prop tighthead)
Appropriately named, these players "prop" up the scrum. During a scrum they are positioned on either side of the hooker.

2: Hooker (Front Row minus props)
This player throws the ball in when there's a line out. He can be found in the center of the line during a scrum where he tries to "hook" the ball back through the feet of the scrum to the number 8 player.

4 & 5: Locks (Second Row)
Generally the tallest players on the team, they are called upon to catch the ball during a line out. They also push on the backs of their teammates (The 2 Props & The Hooker) in a scrum.

6 & 7: Flankers
(6 is the blind flanker, 7 is the open flanker)
Big and fast, these players are ferocious tacklers. They are essentially a cross between a forward and a back.

8: Number 8
No, that's not a typo. The player who wears number 8 is actually called the "number 8 player." He's positioned at the rear of a scrum, receives the ball from the hooker, and initiates the attack.

9: HALF BACK
The link between the forwards and the backs. He specializes in passing and is responsible for rolling the ball into play when there's a scrum.

10: 1st Five
The player most likely to get all the glory or all the grief. When he receives the ball he has the option of passing it to the center, kicking it for position, or running with it himself.

11 & 14: Wingers
(11 is the blind-side wing, 14 is the open-side wing)
The fastest players on the field and often the player who scores a try.

12 & 13: 2nd five and Centre
(12 is the 2nd five, 13 is the centre)
12 & 13 must be sure tacklers and powerful runners. They should be able to run around opposing players as well as through them.