Bear market rally is a short term upward price movement in a strong downtrend or bear market. The upward movement is just a temporary bounce before continuing the existing downtrend. You will see this type of rally in a bear market. It’s a pause in a wider downtrend that will eventually take control again.
In other words, it’s considered as a counter trend recovery in stock prices before the market reverses to a new low.
When the stock market declines 20% or more, market participants consider it as a bear market.
Bear market rally is also referred to as a bull trap.
We do not have any official definition for a bear market rally.