A bull market is a market that is trending upward and when people think the asset value will be increasing.
A bear market is a market that is trending downward and when people think the asset value will be decreasing.
When things look like it is good for the market and likely to make the price increase, it is called “bullish”. On the flip side, when things look bad for the market overall and people think the price will decline, it is called “bearish”.
These terms are most commonly used in the stock market, so are definitely not exclusive to the crypto markets.