A drought is the point where the demand for water in a certain environment is greater than the supply of water available for use. While a drought often occurs in periods of no rainfall, the actual definition is much broader.
A meteorological drought is really just one type of drought. It occurs when rainfall is considerably less than a particular area needs. Another type of drought, a hydrological drought, occurs when the water levels of stored water in a particular area get too low for any reason. The last type of drought, an agricultural drought, happens when the crops do not have enough available water in the soil for their sustenance.