A rally is a period in which the price of an asset, market or index sees sustained upward momentum. Typically, a rally will arrive after a period in which prices have been flat or in a decline.
Rallies are caused by an increase in the amount of people buying into a market. That increased demand leads to increases in price. Rallies can occur in both bull and bear markets, with a bear market rally typified as a brief period of upward momentum in an otherwise downward trajectory.