This is no different than when a bank is robbed and banknotes are stolen. The bank might have written down the numbers of the banknotes and those can be published. But most shops won't check those when somebody buys something.
Say I steal 10 bitcoins from you. I go to someone who cleans bitcoins for a cost of 10%. I send them 10 bitcoins, and they send 1 bitcoin to 9 different wallets (keeping the 10th as payment). That alone would allow you to still track it. But now add in thousands of other people sending them bitcoins on the same day, and some random pauses as to when they send the bitcoins to other wallets, and you are no longer able to tell which bitcoins in are associated with which bitcoins out.
Now, do you just get businesses to stop doing business with anyone (any wallet) that has ever received bit coins from the mixer? And there are many mixers out there.
And this is still simplified. You can be governments are monitoring and running statistical analysis on those mixers to try to find people laundering bitcoins associated with especially bad things. I'd even guess some of the bitcoin laundering operations are ran by governments in an attempt to better track the flow of bitcoins.
The value of a dollar bill is the same whether it was used in a crime. But if it has some ink on it, it might provide evidence that the person holding it robbed a bank. The ink doesn't keep the dollar from being usable.
It has to be this way. Otherwise money simply gets taken out of circulation, and people participating in the economy have to worry about whether money is money.
More: https://www.reddit.com/r/Bitcoin/comments/1qomqt/what_a_land...
Well it's quite a bit different because everyone has access to the ledger where you can see what "bills" were stolen and can automatically prevent them from being used.
Bitcoin's blockchain is just a ledger of amounts stored at addresses at points in time.