A "Bad Bank" is a bank---or some type of financial institution---that the government would establish to buy and hold all of the "bad," or toxic, assets other banks and financial institutions want to sell and get off of their books.
Most of these bad, or toxic, assets are mortgage-backed securities that have been losing value during the past year. Actually, one of the greatest difficulties with mortgage-backed securities during this financial crisis has stemmed from the fact that nobody has been able to come up with an accurate value for these assets.
Ideally, setting up a "Bad Bank" would help solve this problem because the "Bad Bank" would have to come up with a price it was willing to pay for the bad assets---thus setting a value for the assets that everyone could use in their valuations.
Ideally, if the government sets up a "Bad Bank" to buy up all of the toxic assets, investors will be more comfortable investing in banks and buying their stock because the risks associated with doing so will have been diminished.
Unfortunately, determining which assets are toxic today and which assets will be toxic in the future is a difficult task, and it will be tough for banks to shed all of their risk associated with mortgage-backed securities, etc. While nobody is expecting perfection here, the remaining risks may be enough to keep bank stock values depressed for some time.