Disquisition is a long and elaborate word to describe a long and elaborate analysis of a given topic. If you launch into a disquisition about toe jam at a party, you'll soon be talking to a wall.
If you write a paper that looks at every single aspect of a topic, that essay can be called a disquisition. If you have a strong interest in something, chances are your friends and family have heard you give passionate disquisitions on it. A disquisition is an incredibly thorough reporting on a topic. Think of it as a discourse or a discussion of an inquisition or long investigation.