A bear market, by those who deal regularity in the financial market, is when a financial instrument falls 20% from its all-time high. It is named a bear market, supposedly for the way a bear attacks its prey by swiping in a downward direction. Who knew? So, markets or stocks with falling prices are called bear markets.
In some instances a bear market is simply a market in which security prices are falling, so much so that it induces even more selling. During a bear market you will have widespread pessimism and terrible market sentiment. This sentiment is what causes the encouragment of more selling. There is no specific timeframe on how long a bear market can last. Some can last for years (cyclical) and others just a couple of weeks (secular).