The captain is the nominal head of a team during match play.
In national formats, the only specific role of the captain is to choose the team's answer on bonuses if multiple, distinct answers are simultaneously directed at the moderator. In theory, therefore, a captain must be designated at the start of every match (though it can be changed at substitution opportunities); however, this is not always observed.
When captains are designated, they also often coordinate teams' bonus conferral, give default answers and guesses, and so on. They may (but need not) explicitly "designate" or "defer to" another player for answers.
In some state-specific or other unusual formats, the role of the captain may be more formal or have special requirements (e.g., being required to give bonus players absent explicit deferral, being the only player allowed to call timeouts or lodge protests).
If a team has a player who is consistently/regularly designated their captain, he/she may take on other administrative responsibilities, such as organizing or running practices, coordinating plans for attending tournaments, and so on.