The vast majority of essays written at university are some sort of argumentative essay. Almost all academic writing involves building up an argument, though other types of essay might be assigned in composition classes.
Essays can present arguments about all kinds of different topics. For example:
In a literary analysis essay, you might make an argument for a specific interpretation of a text
In a history essay, you might present an argument for the importance of a particular event
In a politics essay, you might argue for the validity of a certain political theory