So, what's with all the sweeping?
You asked, so here you go. I've been inundated with curling related questions from friends for the last week. Here's my standard answer to everything.
Short version:
Because the skip is yelling at them to sweep.
PhD version:
I can send you several papers that have titles like, "The motion of rapidly rotating cylinders sliding on smooth surfaces."
Bill Nye the Science Guy version:
If you remember back to physics class, the reason we can ice skate is because the pressure exerted by our weight down on the thin blade causes a localized melting of the ice. This layer of water between the skate and ice allows us to slide along. When it's too cold out, people say it is "sticky ice" because the ice can't melt enough to let us glide.
In curling, the 42 pound rock is flung down the ice and given a slight rotation. Since the whole rock is actually contacting the ice in a 10 inch wide circle that is about 3 mm thick, it acts like the skate blade and melts the ice below it thus allowing it to travel forward.
As the rock rotates, it drags the water film along to the front corner...in other words a clockwise rotating rock will drag the water to the front right corner...which reduces the drag more there thus allowing to rock to move in that direction...in other words a clockwise rotating rock will curl to the right.
When the sweepers contact the ice, they are essentially warming it up so it is easier to melt. This means there will be more melt water under the rock and this results in two things:
1. The rock will travel farther because it moves easier. Estimations vary, but some say as much as an extra 20 feet if done correctly.
2. The rock will have a more even layer of melt water under it so it won't curl as much.
So if a rock is thrown to weakly or it looks like it will over curl (thrown too narrow), the skip will tell them to sweep to compensate. If the rock is thrown too hard or too wide, the skip starts to look for other ways he can use the rock and prepares the list of insults he's going to hurl back down the ice at the guy that threw the stone.
In Olympic caliber curling, you see them sweep almost every stone, which is a bit more than beer league curling. At the novice level, many more stones will be left in play. This results in very high scoring games that are fun. At the Olympic level, if you give your opponent 3 points in one end, you may as well quit. They try very hard to throw "take-outs", which is the term for throwing your stone down with the intention of bumping out your opponents. Those stones are usually thrown very hard and narrow, which means you have your sweepers sweep it to make sure it stays on course.
Also, because the contact surface of the stone is so small, if it runs over a human hair or a piece of lint on the ice, that is often enough to send it glancing off at a 30 degree angle. So sometimes the sweeping is not being done very hard. Its just enough to keep the ice clean.