The manager is a noble that allows players to create and queue production orders. You can rapidly dispatch any number of jobs from the manager screen, without having to add tasks to individual workshops.
The manager also lets a player set up profiles for workshops.
A manager only performs his duties in his office, so it is absolutely necessary to assign one. Since only a meager office is required, a single chair in the dining room will suffice.
If there are 20 or more dwarves then the manager will need to go to his office to "validate" each work order before it is acted on. If a manager is somehow occupied with other things then this might take a while, so in larger forts you might want to disable other labors for your manager, like hauling and cleaning. The manager will also not perform his or her duties if on break, drinking, attending a party, asleep or otherwise incapacitated (perhaps due to wounds).
To see if an order is approved, check the manager screen — approved orders will have a green checkmark, while unapproved will have a red X.