Bullish describes a view, a position, or a market. A bull market is one where dips are bought and most strategies that involve owning things work. The term is also used for specific instruments: a bull flag, a bull put spread.
The image is a bull thrusting its horns upward; the opposite is the bear.
Example: after the index rose 25% from its October low, financial media declared a new bull market.
Related: bear, bull-trap, trend, buy-the-dip