I'm also trying to wrap my head around it, and this is how I perceive it so far. So the chain splits, and I have a wallet.dat file with 1 coin in it. Would I then use a new program to open that wallet.dat file for the BCC coin, and use in my case Bitcoin Core for my original BTC, with the end result 1 BTC in the new BCC wallet program, and the original 1 BTC in Bitcoin Core?