A bull market is basically a stock market index that is trending upwards for a decent length of time. There is no exact definition for how much the market has to go up or how long the upward movement should last for a bull market to occur but usually when most investors are feeling “happy” about their stock investments, a bull market is in progress.
A bear market of course, is the opposite of the bull market – when the market is declining for a length of time or declines very quickly (ie a crash) then that is considered a bear market. One technical definition is that a bear market has occurred once the market drops 20% from the most recent high.
These terms are most often used in the context of investor sentiment and it is not really all that important for most investors to be concerned with the current market phase if they are invested for the long term. The business media in particular likes to use terms like “bulls”, “bears” since they need to make market moves and trends more exciting than they really are. An investor who like to be active with their investing and perhaps engage in market timing will be quite concerned with the market trend.