A bear market is one in which a general mood of pessimism sees a trend of securities prices falling, over a sustained period (rather than a short term correction). The opposite condition is a bull market. Both bear and bull market spirals can become self sustaining. For example, in a bear market, falling confidence leads to selling, which leads to falling prices and losses, that can create further pessimism and further selling.
A bearish investor is one with a pessimistic outlook, while a bullish investor is one with an optimistic outlook.