OK, thanks for the pointer - I guess it was a little unclear. Here's what zerocoin does:
At the moment, every transaction you make on a blockchain is public. People may not know that ViPBVm4sbXT38h9J23GkAWfNKiuPwVUYQX == BorisTheSpider, but they know that at some point ViPBVm4sbXT38h9J23GkAWfNKiuPwVUYQX sent money to VpFumv3VWir4bczH1CVgatrZ7wJLLXauMR who then sent it to a shady organisation, or used it to buy rotten vegetables to pelt Ben Bernanke with.
This exploitation of connectedness to build a picture of what a network of individuals/addresses are doing is exactly what we have seen with the NSA doing traffic analysis and looking for patterns in who is linked to who, extending that to multiple levels, so not only do you now lose all privacy, but you also can get connected with stuff that you know absolutely nothing about and are not involved with. For example, when you send your VTC to an address that later funds a crime, you come under scrutiny even if you are entirely innocent.
Mixing services let you get rid of the linkage between particular pairs of addresses. For example, if we say that Alice wants to send some VTC to Bob, in a way that doesn't let people know anything about that transaction, then Trent can offer to act as a middle-man. Alice sends VTC to Trent, who then sends it on to Bob. To increase the degree to which this process unlink Alice and Bob, Trent can offer this service to lots of people, then he can wait a while after getting Alices VTC, and send it out to Bob in several transactions of different sizes which add up to the correct amount, so now it's even tougher to know whether the VTC that Trent sent to Bob came from Trent himself, from Carol (another user of Trents services), or from Alice.
BUT
How do we know Trent is on the level? Trent could run off with Alices VTC and never send anything to Bob. Trent could be an NSA shill. Trent could be keeping a log of who sent who what, so he can later use this log to extort the participants in the scheme. Trent could be on the level but still have someone come round his house one day and put a gun to his head demanding to know what he knows, and even if he doesn't keep logs, at least his current transactions in-transit would be compromised since he can't discard the information about who needs to receive what immediately - they have to be sent it first.
The existing mixing services are very trustful - they require a third party to act in a trustworthy way, and expose that third party to being threatened, bribed or otherwise manipulated into giving up information.
What if, instead, there was a way, right on the VTC blockchain, to mix coins, so that Alice could make a transaction (or set of transactions) that sent coins to Bob, without any third party being involved, and in a way that makes it impractical to trace that transaction. That's Zerocoin.