Think of it like copying twitter's database then launching a competitor. All tweets, users, etc. on both sites are the same up until the day the database is copied. Then the tweets, users etc. can be different depending on which site folks use.
You get all your tweets on the new site for free.
Same with BCC. They copied the Bitcoin database at block 478558. So if you have a coin in a BTC account before block 478558, you now have the same coin on the BTC chain, and a copy of that coin on the copied BCC chain.
To use it, you just need to use a BCC wallet, the same way you'd use a BTC wallet to use BTC.
But if you don't know your private key (usually because your coin was on an exchange) then you are out of luck. Google if your exchange will credit you BCC.
I've tried explaining this to numerous people but never thought about comparing it to starting a clone of a website with the same DB to start with. Great analogy.
Basically, Bitcoin cash is another kind of cryptocurrency as Bitcoin. The naming is somewhat confusing. If you owned Bitcoin at the start of Bitcoin cash, you get free Bitcoin cash.
There are technical differences that may make one or the other succeed.
