A trader who respects the fact that what goes up must at one point go down a little if not fully. A bear trader is somewhat pessimistic towards a certain security or the economy. In trading activity, a bear profits from the downward movement by shorting or going against a certain security by selling it short.
Market bears are normally seasonal ones for the market in general goes in one direction which is up. Bears emerge from hybernation when the market seems overbought and overextended that it is due for a psychological correction downward to satisfy profits or simply due to bad fundamentals and a technical perspective that favors a correction.