The Frankfurt School is the name given to academics before and after World War Two who worked for the privately financed Institute for Social Research who published their work in the Institute's "Journal for Social Research."
Those academics shared a common -though loose- paradigm. That is to say they "shared the same assumptions and asked similar questions" and were all influenced to some extent by the dialectical philosophy of Hegel and Marx.
So what are the key features of Critical Theory?
Firstly, the Frankfurt School approached questions of morality, religion, science, reason and rationality from a "variety of perspectives and disciplines simultaneously." Bringing these different disciplines together would yield additional insights, it was argued.
Secondly, Critical Theory claims to be reflective/inherently self aware. Critical Theory reflects, in other words, on the "social context" which gives rise to the theory in the first place, on the function of that theory and on the aims/interests of practitioners.
Finally, Critical Theory is -as its name suggests- CRITICAL. The task of theory is not just theoreti cal. It is also practical. The aim is not simply to understand (i.e. diagnostic) but also to change (i.e. to be remedial). Critical Theory can create social and political conditions more "conducive to human flourishing."
For further reading see Finlayson, HABERMAS, Oxford University (2005)