"It sort of make sense more in context, i.e. over the arches below. Think of Bramante basically wrestling with two "problems" of the classical language: the relationship of column and wall (each of their natures, how they interact, turn the corner, etc.), and trabeation vs. arcuation. Imagine him using this courtyard to both pose these problems to himself, and offer some "solutions:" columns retain their full integrity when associated with pure trabeation (their proper, Vitruvian condition), but trabeation can't span as far as arcuation (thus the photo, with column centered over the arch below); pilasters are somewhere between columns and walls, but properly support trabeation, thus the engage order below; and then the whole turning of the inside corner problem.
Some things to read: Arnaldo Bruschi's book on Bramate, and Peter Murray on the Italian Renaissance (for the corner problem)."