Toxic assets are high-risk financial paper. In one sense they are a 'bad debt' but in a complicated way.
This explanation is a good one, from Yahoo (I have re-phrased it):

Bob borrows $200,000 at 6% interest on a house worth $275,000. The bank now has 'mortgage paper', and can sell it to get working capital to make more loans- a normal procedure.
The house loses value in a falling housing market, say down to $150,000. Bob can't pay the mortgage payments.
The bank can't sell it, so it becomes a 'toxic asset'.

If the mortgage had been sold to a large institution by Bob's bank, and that large outfit and others (RBS, Bear Stearns, etc.) had bought a bunch of similar 'paper,' then they have 'toxic assets' at a level that might require government intervention to prevent collapse of the banking and loan system.

The assets are still there, but in the present market they are worth a fraction of the original value. If the economy turns around, they may again go up in value, but almost never to the original value.

Let's hope that governments are able to put controls into banking that will prevent similar occurrences in the future.