Social theory is what people do when they try to figure out how the social world works.
In effect, this means that social theory is what happens when people take the social as an object of study. Marx, Weber, and Durkheim, to take only the most famous, are considered to be social theorists because they tried in their writings to make sense out of the social world. Studying social theory means to read and write about what social theorists have written. When you do this you are joining an on-going conversation about the nature of the social. Contemporary social theory is usually thought to refer to what social theorists have written since about WWII, or 1950.