The offensive coordinator in football is the coach in charge of the offensive unit. The responsibilities of offensive coordinators include leading the offense during practices, designing plays and strategy, and calling offensive plays during football games. Offensive coordinators report to the head coach. Below is a chart showing the structure of power within a football team's coaches.
The following all report to the offensive coordinator
In most cases the offensive coordinator is responsible for the play calling of the offense. They decide the formations and plays that they want to run. They work with the team's quarterback, designing the system they want to run and one that the quarterback feels comfortable in. Longer tenured quarterbacks have more of a say in the play calling.
There are times though that the head coach will take over the duties of play caller if they feel they can do a better job.
Given their importance an offensive coordinator in the NFL is currently making around one million dollars per year. College football teams pay their offensive coordinators slightly less, between 200 and 800 thousand dollars per year.
It is quite common for a good offensive coordinator to be pursued and hired by another team as a head coach following a successful year.