A bear market is one in which the prices of assets are falling or expected to fall. A bear market usually occurs when the economic environment is deteriorating or in time of financial crisis. The opposite of a bear market is a bull market.
Bear markets are not unusual. For example, over the last century 26 bear markets have occurred in the United States (so once every 4 years on average). Their severity varies as well as their length. One famous bear market is the one we experienced in 2008 during the great financial crisis.