What are tainted coins exactly? I've come across the term of a tainted coin several times now.
I understand that coins, or better, the origin of a coin can be traced throughout the blockchain. 

I've read that bitcoins can be disassociated from an address, by sending it to a sufficiently large enough wallet which handles many transactions, thus making a transactions origin "untraceable".

This collides with my understanding of the blockchain, where each transaction can be tracked back to its origin. 

What does the concept of a tainted coin mean in this context and how can a coins taint be measured?
You can trace the coin back to its origin, the question is whether that information is meaningful.

Say I steal 50 bitcoin. I can pass them around between several different Bitcoin accounts, all mine, and you can trace them. The problem is, you don't know whether any of those transactions are real.

Say Jack has 50 bitcoins that come from a block reward and are untainted. Now, say Jack and I both deposit our 50 bitcoins in a web-based wallet. And say Jack withdraws his 50 bitcoins from that web-based wallet and he gets my 50 bitcoins.

Jack now has 50 bitcoins that you can trace to a theft and are therefore tainted. But Jack has done nothing wrong and it doesn't do any good to be able to track his bitcoins because I, the bad guy, now have untainted bitcoins.