The grim name comes from the idea that even a dead cat bounces if dropped from high enough. After a large decline, short covering and buy-the-dip reflexes produce a rally that has no fundamental support.
Distinguishing a dead cat bounce from a real bottom is only possible in hindsight, which is why bear markets are hard to trade from the long side.
Example: a stock falls from $100 to $40 on an accounting scandal, bounces to $52 over three days, then declines to $25 over the next month.
Related: bear, buy-the-dip, capitulation, short-squeeze