With a mixer, the hacker can obfuscate their identity before using the service. The mixer will attempt to break the linkage between the coins that were sent to them and the coins that are sent to the destination address. It's not a foolproof way but it is able to make your coins untraceable to a good percentage. If done correctly, there shouldn't be an easy way to prove that the coins were once from an X hack for example.
To complement the idea that Bitcoin should help with the user's privacy. Mixer breaks the linkage of the coins and outsiders won't be able to track where the coins came from. This helps to obscure the user's spending habits for example.