I thought that hegemony explains how one class exerts influence over another, and interpellation explains how one class allows the other class to exert influence over them. But then the two seem so similar.
The concept of "hegemony" is usually associated with Gramsci (especially his Prison Notebooks) and "interpellation" with Althusser (Ideology and Ideological State Apparatuses). The latter was influenced by the former. Both concepts are motivated by the same question: Why is it that the proletariat does not revolt as Marx predicted?
Hegemony could perhaps be conceived as a state of affairs: the success of the dominant class in making their view of the world (ideology) accepted and internalized by others as their own.
Interpellation, on the other hand, is a process of such internalization (subjectivation). Althusser writes that
ideology ‘acts’ or ‘functions’ in such a way that it ‘recruits’ subjects among the individuals (it recruits them all), or ‘transforms’ the individuals into subjects (it transforms them all) by that very precise operation which I have called interpellation or hailing, and which can be imagined along the lines of the most commonplace everyday police (or other) hailing: ‘Hey, you there!'
Assuming that the theoretical scene I have imagined takes place in the street, the hailed individual will turn round. By this mere one-hundred-and-eighty-degree physical conversion, he becomes a subject. Why? Because he has recognized that the hail was ‘really’ addressed to him, and that ‘it was really him who was hailed’ (and not someone else).