I do not normally have season long team Captains on recreational teams. I have found there is enough practice to practice turn over that we just pick new captains for each game. Which means, that in reality we do not have team captains for the rec teams. When I do establish one or more team captains for a team here are my expectations.
The team captain must embody the team values. Each team has a unique set of stated and unstated values. The team captain has to embody those values both on and off the field. As a leader on the team it is critical that the team captain grows those values in the team. Therefore, it is also my expectation as part of this that the team captain clearly communicate his or her desires for stated team values when we are formalizing them. It is also my expectation that she holds her teammates to those values primarily by example, but sometimes by discussion.
The team captain has to be able to communicate my intent to the team and the team's intent, concerns and ideas to me. When I do not communicate a point well, the captain should be able to help translate my intent to the team. More importantly though, the captain should be able to tell me easy and hard "truths" from the team. Easy truths are feedback from the team on practices, playing style and etc. Harder truths are criticisms from the team about me or my leadership from the team. These are vital for me to hear while keeping the player or players who provided the feedback anonymous. It is this facilitation of hard truths that will critically help us stay together as a team and overcome any challenge.
When I do not have an assistant coach, you need to perform that duty. You may need to run practice or coordinate with the team. If I am running late for a game you may lead to teams preparation for the game. In my absence you need to be the one keeping the team running.
This is an exceptional opportunity for you to develop and experiment with your style of leadership. Try new things and see how they work. Have the courage to stand in front of the team and say "follow me" and try whatever idea you have.