Holmes is revered as a quasi-deity among most legal academics, and while I think he's entitled to far less respect than he generally receives, I've always appreciated this sentiment. Basically, "the simplicity on the other side of complexity" is the lawyer's way of stating "it all adds up to normality."

So, the simplicity on this side of complexity would be something like naive free will theory -- basically, "it feels like I have free will, so something magic must happen that gives me true power to choose." If you reject this simplicity, but don't make it to the other side of complexity, you might end up saying silly things like "free will doesn't exist, so all of our choices are meaningless -- everything is determined for us." You need to work your way through the complexity to reach the simplicity that says "yeah, the experience of making decisions is real, and that's what matters -- this is just a normal part of physics, not something magic." Sometimes, simple truths really are correct -- but you need to work through a bit of complexity to understand why that's the case.