The younger ages, Instructional and Shetland, the parents a lot of times like to bring a snack and drink for after games for the team. The Team Mom will usually keep a schedule of what parents are bringing snacks for what games so you don't have too many parents bringing items on the same day. The Team Mom will sometimes help out in the dugout with the kids while the coaches are in the field.
The Team Mom's responsibility is a personal preference of what you want to do and how involved you'd like to be. Talk to your coach about your ideas, your coach will appreciate any help he/she can get. You are an important part of the team and everyone will appreciate your role with the team.
I only wrote this because I've seen questions asking what a Team Mom is expected to do and these are just some of the things that my Team Moms have done for teams in the past.