Obligation means the act of binding oneself to some duty, to some contract, to some promise. It is binding someone to do something. Obviously, it arises out of a sense of duty. That is why, one may see an analytical connection between obligation and duty, the former having the same meaning as that of duty. To be obliged means to have a duty. An obligation can also be the act of obliging oneself else. In such a case, a duty is the conception of some behavior as the object of an obligation. People are obliged to perform their duty. There cannot be an obligation without a will imposing a duty or an obliging will.
Obligation, one may see clearly, is a two-way situation. It is a relational concept. It is used (a) for a relation between individual person. One is, for example, under an obligation to someone else; people are, or say used to be, greatly obliged to one another. It is used (b) for a relation between a person and an institution, such as the government. To be under an obligation to someone (say individual or government) may to be owe something (in case of an individual’s obligation to a government it may mean ‘to owe obedience’). In case of an individual’s obligation to the state or the government, what is amounts to is that the state or the government has corresponding rights over the individual.
To understand the term ‘obligation’ more clearly, it is better to relate the term ‘obligation’ to ‘bound’ than to ‘owing’. We may be bound to perform some action without in an obvious sense owing anybody anything. To be ‘bound’ is not be in bonds. What at best it means is acceptance of a submission, or say losing a certain amount of freedom. When we accept submission, we accept to work within certain limitations, and such a submission remains until obligation stays; a certain amount of lost freedom is not regained until the obligation has been discharged.
So understood, the concept of obligation includes, if one seeks to identify its inherent implications, (i) an act of binding oneself to some duty, (ii) a situation characteristics of a relational relationship, (iii) an authority, say the government with assured rights over the individuals, and the individuals, agreeing to obeying the laws of such an authority.