The story most often told relates to how each animal is said to attack. A bull will thrust its horns into the air, while a bear will swipe down. These actions metaphorically reflect the movement of a market, with bull markets trending up and bear markets trending down.
In the jargon of stock-market traders, a bull is someone who buys securities or commodities in the expectation of a price rise, or someone whose actions make such a price rise happen. A bear is the opposite someone who sells securities or commodities in expectation of a price decline.