obligation
1 : an act of making oneself responsible for doing something
2 a : something (as a promise or contract) that requires one to do something b : something one must do : DUTY
3 : a feeling of being indebted for an act of kindness
http://www.wordcentral.com/cgi-bin/student?book=Student&va=obligation
I have an obligation to help my friend with his science project because I promised him that I would.