A stock market "bear" is an investor who believes that a particular stock or market, or the market as a whole, is headed downward. Bears often try to profit from a decline in prices. The term can be applied to many markets, including commodities/futures and bonds.
An investor who believes a particular stock or market will trend downwards is referred to as "bearish" on that stock/market.
The opposite is a "bull", who believes that the market or a particular security will go up.
In the long term, the stock market has had a bullish trend.