Exigence is your driving force behind writing, the cause that prompts you to write that document. I always likened it to purpose, but exigence is more than that. It holds with it a sense of emotions and responsibility, that this is the reason behind the cause. It is the direct motivation that drove you to write. An example of this in use would be the memo, in which we had to choose a topic which we felt strongly about around campus. Our reason behind what we chose was the existence of the document. Writing the engineering proposal followed a similar process as the memo. I chose a topic which I felt strongly about in order to fully express in my own words.