Bears are traders who believe that a market, asset or financial instrument is heading in a downward trajectory. In that regard, they hold an opposite view to bulls, who believe that a market is going upwards.
Bearish traders believe that a market will soon drop in value, and will attempt to profit from its drop. They will usually do this by short selling the market. This puts them in contention with bulls, who will buy or go long on a market in the belief that doing so will return a profit.
Spotting when a bear market is taking hold or coming to an end is key to both profiting and limiting loss when trading.