Explanation in science is not just a matter of revealing the full detail of the parts and processes of mechanisms. Explanation is many things, as evidenced by the literature on the topic in philosophy of science. Most commonly, explanation is sought to reveal causes, and the contemporary discussion of mechanisms contributes substantially to this discussion. A different idea is that unification is explanatory—and yet explanation by unification is a multifaceted and disputed notion.
I think FEP explains by unification because it is a principle that increases our understanding of many very different phenomena, such as illusions, social cognition, the self, decision, movement, and so on (see The Predictive Mind, Hohwy 2013, for examples and discussion). FEP teaches us something new and unexpected about these phenomena, namely that they are all related as different instances of prediction-error minimization. For example, we are surprised to learn that visual attention and bodily movement are not only both engaged in prediction error minimization, they are essentially identical phenomena. FEP thus explains by providing a new, unified and coherent view of the mind.
In this manner, FEP is explanatory partly in ways that are separate from mechanistic explanation, and also from the discussion of how the functionalist and mechanistic approaches relate to each other.