I think the idea would be that you ask your credit card to convert $10 into 10 untraceable tokens, and then spend them one at a time. You do a handshake dance with the credit card company so you walk away with tokens that only you know, and you have assurance that the tokens are in the same pool as everyone else who asked for untraceable tokens from that credit card company.

Then you can go and spend them freely. The credit card company (and maybe ever third parties?) can verify that the tokens are valid, but they can't associate them with a user. Assuming that the credit card company keeps a log, they can also verify that a token has never been used before.

In some sense, it's a light-weight and anonymous block chain.