Wittgenstein's Philosophical Investigations indeed is a foundation for a school of thought in sociology, called social constructionism (or constructivism). One field in sociology is identity question, that is, "How do we identify who we are in terms of our gender, race, and ethnicity?" One popular answer is called social identity theory which asserts that social groups are real and exist prior to individuals. Self-identity, according to this view, obtains through social group realism.
Some sociologists however believe that this picture of self-identity is wrong since one's group identification tends to be fluid and under-determined. According to them, we identify where we belong not by virtue of pre-existing social groups, but by socialization (e.g., upbringing). To reject the social-group realism, these sociologists need theoretical backing, and they find it in Wittgenstein theory that the meaning of a word is its use in the linguistic community.
Consider 'Santa Claus'. Santa Claus does not exist, but talking about him has perfect meaning. To Wittgenstein, it does not matter what image of Santa Claus we have in our head. What matters is that we understand sentences that include 'Santa Claus' and know how to use the word properly in our linguistic behaviors. So long as people in the linguistic community understand sentences containing 'Santa Claus', they can be said to know what the word means. This idea of Wittgenstein is called meaning as use theory. Social constructionsts apply this theory to argue that the meaning of race or gender depends on how the linguistic group use the words, thus the outcome of the social construction.
