What Does It Mean When Someone Is Obligated To Do Something?

When you are obligated to do something, then is is your duty or job. You are right. You must promise to do something because it is your obligation.

  When someone is obligated to do something it means they have agreed to do something or a situation they are in requires them to do something.  It is similar to a duty or responsibility.
  Example:  If I go to the car dealer and decide to buy a car, but I don't have enough money the dealer might arrange a loan for me.  If I accept the terms of the loan I become obligated to make payments to the lender in the amount and by the date due.  If I fail to meet my obligation the lender has the right to repossess my car and sell it to get their money back.
  Example 2:  If my dog digs under the fence and gets out of the yard and goes across the street and kills one of my neighbors chickens then I am obligated to replace the chicken or pay my neighbor a fair price for the damage.  If I don't, my neighbor can take me to court and have a judgement placed against me and if I still didn't pay I could be put in jail.
  Those are examples of financial and legal obligations.  There are also family obligations (do your chores, come home for the holidays, attend a wedding), social obligations (similar to family, but for friends), and religious obligations (do what you are supposed to do, don't do what you are not supposed to do.)

For example someone may be obliged to offer something regardless of weather you say yes or no or like obligated say if in a job description duties then they would be obligated to do so