A mixer takes a group of coins and shuffles them so that the output is hard to trace back to a specific input. The idea is to break the line between where the coins came from and where they go. CoinJoin does the same thing with a protocol rather than a service, which removes the middleman but also removes the place you would complain if it went wrong.
The honest limit is that mixing helps the coins and not the person. If you mixed coins that came from an exchange that knows your name, the exchange still knows your name. Mixing breaks the chain on the ledger. It does not erase the record at the point where the chain started, and that is where most traces actually begin.
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