Usually the third holds the broom while the skip throws. That's why the third is also called the "vice skip." The third holds the broom because he or she is usually the next most experienced person on the team, after the skip.
Really, though, there aren't any rules about who must hold the broom, when. The lead could hold the broom the whole game (except when he's shooting, of course) if that's what the team wanted.
On some teams, the third might actually be better at "calling ice" (showing where to aim) or making sweeping calls, so they might have the third hold the broom throughout the game, instead of the skip.
Well, darling, in the sport of curling, you've got the lead, second, third, and skip. The lead kicks things off, the second clears the path, the third sets things up, and the skip calls the shots. It's like a dysfunctional family where everyone has a role to play.
The Vice Skip throws the fifth and sixth rocks of the end, holds the broom for the skip, and is responsible for scoring and determining which rocks are closest to the middle. Additionally, according to traditional rules, the Vice Skip is the only player on the team allowed to go behind the house with the skip. The Lead and Second are to remain between the two hoglines during the game.
They are the third player to throw rocks for the team. The "lead" throws the 1st and 2nd rocks, the "second" throws the 3rd and 4th rocks, the "third" throws the 5th and 6th rocks, and the "skip" throws the 7th and 8th rocks. The third is also sometimes called the "vice skip," because the third acts as skip while the skip is throwing his (or her) rocks.
MLB player Skip Schumaker throws right.
Skip James is 6 feet tall. He weighs 185 pounds. He bats left and throws left.
Skip Pitlock is 6 feet 2 inches tall. He weighs 180 pounds. He bats left and throws left.
Skip Dowd is 5 feet 10 inches tall. He weighs 160 pounds. He bats right and throws right.
Skip Guinn is 5 feet 10 inches tall. He weighs 180 pounds. He bats right and throws left.
Skip Jutze is 5 feet 11 inches tall. He weighs 190 pounds. He bats right and throws right.
Skip Lockwood is 6 feet 1 inches tall. He weighs 175 pounds. He bats right and throws right.
Skip Schumaker is 5 feet 10 inches tall. He weighs 195 pounds. He bats left and throws right.
All members of the curling team throw stones. Every end, they take turns throwing 2 stones each in the order of: Lead, Second, Third/Vice/Mate, Skip. The person who is currently delivering their stone could be called the thrower.