A period of sustained increases in the prices of stocks, bonds or indexes. This type of price movement can happen during either a bull or a bear market, when it is known as either a bull market rally or a bear market rally, respectively. However, a rally will generally follow a period of flat or declining prices.
A rally is caused by a large amount of money entering the market, bidding up the prices. The length or magnitude of a rally depends on the depth of buyers along with the amount of selling pressure they face. For example, if there is a large pool of buyers but few investors willing to sell, there is likely to be a large rally. If, however, the same large pool of buyers is matched by a similar amount of sellers, the rally is likely to be short and the price movement minimal.
Source: Investopedia
Some consider a rally moving 20% up to be a new bull market.