Certain events can affect a stock and change its current trend. For example, a stock can be in an uptrend but a particular event may be considered bearish in that it may reverse the trend from up to down. Events can also be viewed as bullish or bearish for the entire market.
Certain technical patterns are bullish or bearish. For example, a stock can be down but form a pattern that is bullish because it forecasts a reversal of the downward trend. The whole chart may be bullish or bearish in that it reflects the current direction of the stock.
Market pundits and talking heads like to proffer outlooks. Their opinions can be bullish or bearish depending on where they think the market or a particular stock is or should be headed.
When someone believes that the market should be going up (or down) -- regardless of what the market is actually doing at the moment -- they are said to be bullish (or bearish) on the market. Investors can also be bullish or bearish on a particular stock or sector.
A Word of Caution
Do not confuse opinions with trends. As legendary trader Jesse Livermore used to say: "Markets are never wrong -- opinions often are." If the market is in a bullish trend, it's indisputable. But someone might think that the market should not be going up, or that it has gone up too far and should be going down. The fact that someone is bearish does not necessarily mean that they are correct.