In simple explainations, a bull market means that the market is getting stronger (stock price increase. etc) while a bear market means the opposite (stock price falls). Many news casters use this terms because it is a more colorful way of explaining the market.
There are many theories about it, but the best and most generally accepted explaination I heard is this!
This is probably derived from ancient animal fighting matches where ancient romans were actively engaged in bull fighting competitions, and the English did bear baiting (basically almost the same thing as bull fighting), since the bulls and bears are such aggressive animals that they are used to dramatize market changes (it is certainly less interesting if your average CNBC newscaster say the market is just going up or down right?)
In their fights, bulls generally charge up, and bears, being tall animals, have to swipe their claws down and maul the animal.
Hope this has been interesting and I hope to do more of these fun facts for you guys. Like or share this trival piece of knowledge and entertain your fellow traders!