Sweeping makes curling a team activity, and allows all four players on the team to work together with the goal of reaching a better outcome for each shot than can be achieved without sweeping

You sweep for two reasons:

• Distance (weight) -  Sweeping reduces the friction between the ice surface and the stone, and will allow a stone to glide up to 15' farther than it would have without sweeping.  This is about 10% of the total distance (126' to the center of the target) that the stone will travel.
• Line (curling trajectory) -  Sweeping delays the "curling" action of the stone and straightens the trajectory it travels (again through a decrease in friction), allowing the team to control how much a particular shot will curl (or curve). This allows teams to accurately curl stones behind other rocks, or to hit opponents' rocks with tremendous accuracy.

The main problem people often have with sweeping is that one can easily over-sweep a stone. Good curlers need a keen sense of observation to know when to sweep, and when not to sweep.  Some curlers even use stop watches to inform them of the speed of a rock.

Additionally,  a delivered stone that is too heavy makes sweeping useless.  It is traditionally best to deliver your rock with 90% to 100% of the distance/weight needed on a draw shot, allowing your teammates to sweep the stone (if needed) to the precise desired distance.

To see what Olympic Curlers Debbie McCormick and John Schuster have to say about sweeping  click here.