"Bulls" are traders who earn from the rising prices of assets. Bulls buy cheaper, wait for the price to rise, and then sell at a higher price. For example, bulls can buy Bitcoin at $28,500. When the price of Bitcoin rises to over $30,000, they sell it and pocket the difference.
The bull market is a time when a rising trend dominates it, meaning that prices of coins are increasing. Buyers earn, while in the derivatives market, holders of long positions on futures contracts profit.
"Bears" are traders who earn from the falling prices of assets. Bears open short positions in the futures market and also "short" coins in Spot trades. The rules of short selling are such that the trader borrows coins, sells them at the current price, and when the price of the coins drops – buys them back and returns the debt. Profit is made if the buyback price is lower than the selling price. If a trader borrows assets and the price rises – they will have to buy back the crypto at a higher price to return the debt.
For short sellers, the opportunity to profit comes with a bear market. During this period, asset prices fall, and crypto becomes cheaper.
Learn more: Crypto Futures Trading: How It Works