hey, I'd like to know too...it's not like I ever got to play on a football team. Always wondered why they say a HC in football is the most influential coach in sports
They set the tone and the team philosophy. Most of their work is done during the week and in the off season. In games, and it depends on their relationship with the OC/DC/ST coaches, they might only suggest plays and say when to kick it/go on 4th/use timeouts vs all the way up to taking over calls themselves.
Practice times, Strength training philosophy and schedules, player recruiting/acquisition (in college), player development, depth charts, sitting injured players - all HC
They're more like a CEO, in that they hire people they trust in the active roles (OC & DC) then depending upon how the team performs they make adjustments whether it's giving a tired team a break or upping the tempo when the team needs a boost. If a team comes out flat it's usually the HC's fault.