This term may refer either to the market or traders' behavior. It originates from a real bull who attacks upwards with its horns, which is a metaphor for pushing prices up.
Bulls are traders who are optimistic about the asset price and believe in its upward direction. They usually open long positions intending to sell at the peak price. When the quotes are increasing in price, the market becomes bullish. It is next to impossible to predict when this happens, so usually, it is claimed to be a trend as it occurs.
The confidence among traders rises; people start investing more and take higher risks. It happens as a result of the strong or strengthening economy. Unfortunately, it is difficult to foresee the possible change to the bearish market. You should always keep an eye on global events: possible trade wars, political inconsistencies, social tension. All of these may point at a likely bearish trend.
Beware of a bull trap that is usually created by traders of stocks and commodities when they buy large amounts of assets to imitate the upward movement. Once in a bull trap, traders buy shares at high prices in hope that they will rise soon. However, most of the time, the market either drops or stays at the same level.