A "Chinese Wall" is most commonly employed in an investment bank, where such banks offer Corporate Finance services to companies (managing the fund-raising, for example), and at the same time also provide Financial Research information to a more general audience.
Because it is possible to manipulate the Financial Research reports to encourage the general public to purchase shares in a company (for example), the conflict of interest arises when such a company is also the customer of this particular investment bank.
In fact, despite Chinese Walls (named after the Great Wall of China), these situations of conflict of interest allegedly arose during the heydays of the "dot com" gold rush, where research analysts essentially marketed companies which they, or related parties, own shares of. By putting out positive research advice, or even simply by choosing to talk about their client amongst the thousands of possible companies they might have discussed, the share price of these companies could be boosted without regard for actual financial worthiness. In a way, this was one of the many factors contributing to the dotcom "bubble" which eventually burst around the first half of 2000, resulting in a lengthy sluggishness in world markets for years to come.
The U.S. government has since recommended modifications and improvements made to the Chinese Wall concept, to hopefully prevent such grevious dereliction of duty by research analysts and their banking employers.
There are some who critique the Chinese wall, saying that it prevents some small companies from being properly valued, since without the ability to get exposure via a tie in with the investment bank, most investors would simply not know about them.