Some people want to change the rules. But some other people don't want them changed. So now we have two sets of people, the Changers (XT) and the Don't-Changers (Core) who will be following different sets of rules.
So their softwares won't play together in places their rules disagree. This will create a "fork" in the ledger histories. If your coins existed before the fork, everyone will see them. But if you transact them in a way that's incompatible with one set of rules, the transaction will only exist on one side of the fork.
So the public will then have to choose which side of the fork to live on. They will probably want to live on the dominant side. Then the losing side will give up and switch!
Bitcoin-XT actually has a few built-in mechanisms to make this transition graceful. It will only deploy the incompatible rules once it has a 75% majority vote, and is thus confident of success.
Practically speaking if you own Bitcoin prior to the fork I believe it means you will then be able to use your coins on both post 'fork' versions. Once the fork happens you will have to decide which version you want to transact on when you receive new coins.
It remains to be seen which version will survive, or if perhaps both versions will.