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