When Althusser first introduced the concept of interpellation, in Ideology and Ideological State Apparatuses, the Marxist philosopher was referring to the police act of interpellating someone: "Hey you!", and the subsequent turning backward of the guilty subject(person). Althusser thus pointed out the essential relationship between guilt and subjectivity, as Nietzsche had done in his On the Genealogy of Morals. As in Foucault's philosophy, the subject is not preexistent to its constitution by power or ideology.
In the context of Social Science to be Interpellated is to identify with a particular idea or identity. For example, if someone were to shout your name at you in the street, you would recognize that salutation to mean yourself. It is basically thinking 'that means me'. It is the process by which you recognize yourself to belong to a particular identity.
This has been a particularly useful insight for understanding the power of media; the extent to which media (especially advertising, but also news and entertainment) "speak" to viewers by addressing them is a part of their emotional and persuasive appeal. In this context, the interpellation is rarely as specific as being addressed by name, but rather being addressed as a member of an audience, in terms of a specific demographic, or as a part of a subculture. When we recognize that we are being spoken to, we not only engage more deeply with the text, we also accept the social role being offered to us: young, white, female, gay, athletic, liberal, etc.
The word Interpellation is also used to refer to the formal right of a parliament to submit formal questions to the government. In many parliaments, each individual member of parliament has the right to formally submit questions (possibly a limited amount during a certain period of time) to a member of government. The respective minister or secretary is then required to respond and to justify government policy. Interpellation thus allows the parliament to supervise the government's activity. In this sense, it is closer to a motion of censure.