Writers often think of paragraphs as units of length, but the paragraph measures something more abstract than inches of paper: it measures ideas. Each paragraph in an academic paper acts as a concrete unit of the central argument. Every paragraph advances a new claim, building on the claims that have come before, until the writer conclusively establishes the position of the entire paper. See below for more examples and explanation!
Writecast, the Writing Center's podcast, also has an entire episode dedicated to paragraphs!