In its narrow sense, the research programme of the The Frankfurt School — a form of social theory that, unlike "traditional" theory, aims not merely to describe society but to disclose the hidden forms of domination within it and thereby contribute to human emancipation. Horkheimer laid out the distinction in his 1937 essay "Traditional and Critical Theory": the former takes existing institutions as given; the latter asks whose interests those institutions serve and whether different arrangements are possible.
In its broader contemporary sense, "critical theory" has come to name a much wider family of traditions that share the basic emancipatory impulse but work from very different theoretical foundations: Frankfurt-style Critical Theory, Foucauldian genealogical critique, Gramscian cultural analysis (Antonio Gramsci), post-structuralist critique of discourse, postcolonial theory, feminist theory, critical race theory, and various hybrids. What unites them, roughly, is suspicion toward claims of natural, neutral, or universal authority — and attention to how power operates through knowledge, language, culture, and institutions as much as through overt coercion.
The unity is sometimes overstated. Habermas's rebuilding of Critical Theory on the foundations of communicative rationality is in key respects opposed to Foucauldian genealogy, and many contemporary "critical" theorists would have been unrecognizable to Adorno. Critics on the liberal side (Richard Rorty, Thomas Nagel) have argued that the broader project has often substituted hermeneutic suspicion for constructive political argument. Defenders reply that the point is precisely to denaturalize — to make the contingent visible as contingent — and that constructive proposals belong to politics, not theory.