There are many responsibilities that come with parenthood, but here are a few:
always being the good example for your children
making sure your children have all of the basic resources that they need (food, water, clothing, etc.)
being involved in their lives ( coming to class plays, award ceremonies, talking to them about their day, etc)
Protecting them from harm
Making sure they have the proper education that they need
Giving them advice when they need it most (overall just being their support system)
These are just a few, let me know if you need anything else! I hope I helped! :-)