The phrase "separate peace" is a military term, and it's a bit complicated. If one nation has an alliance with another nation, it can refuse to fight that other nation's enemy by forming a separate peace. In other words, your best friend Betsy is at war with that pain-in-the-butt chick from shop class, Chelsea. As Betsy's friend, you're supposed to fight her battles with her, but you form a "separate peace" with Chelsea so that you can remain a bruise-free spectator. You're still allied with your friend Betsy, but you're out of the fray.
Now check out the one mention of this phrase in the novel, at the end of Chapter Nine: "It wasn't the cider which made me surpass myself, it was this liberation we had torn from the gray encroachments of 1943, the escape we had concocted, this afternoon of momentary, illusory, special and separate peace." These lines offer us a second meaning, and this one with less military jargon. Just take the term literally – a separate peace. A peace that is separate from the rest of the world, isolated somehow, protected. Sound like Devon? Like youth? Exactly. The rest of the world is at war, but Gene and the other boys at Devon have achieved a peace outside of that war, a peace that is separate from it.