Rather than starting with axioms that lead to a sort of universal knowledge, Foucault did studies that could be considered more sociological in nature to show how relations of power affect the way that we experience ourselves and others, i.e., how it fashions our subjectivity. This is what he terms his "archaeological" method in articles like "What is Enlightenment?" http://foucault.info/documents/whatisenlightenment/foucault..... Examples of these studies include his works Discipline and Punish and The History of Sexuality.
At the very least, Foucault's studies show how some of the most significant ways in which we experience the world and ourselves are socially constructed, rather than essential. Identity then becomes political, rather than something that is distinctly our own. In some of his work, he also directly takes on thinkers like Kant in an attempt to show their work as historically situated rather than universal.