Ok, I understand what a mixing service does. But what is the reason to "confusing the trail back to the funds' original source". When and why do I need to use it?
A necessary arguably-detrimental feature of Bitcoin is that all transactions are published, so everyone can know where everyone else's coins came from and went. Coin mixing helps prevent people from knowing where your coins are coming from and going, especially for reused addresses.
For example, if you're running a Respectable Business and play SDice with the investments, you want to mix the coins when you get them, have them go to a separate wallet where you send to SDice, then mix any winnings again and have them pop back into the "business wallet." Then, "Oh, look, we made 10BTC this week."
Alternately, maybe you're buying illicit goods, but have all your funds on an address attached to your name somehow. Using a mixing service, you can send your coins there and have them go where they need to be to buy what you want without anyone knowing anything except possibly that you sent your coins to a mixing service.
Or maybe you just want a sense of privacy.
