A tropical cyclone is the generic name for any "non-frontal synoptic scale low-pressure system over tropical or sub-tropical
waters with organized convection (i.e. thunderstorm activity) and definite cyclonic surface wind circulation" according to the FAQ at http://www.aoml.noaa.gov/hrd/tcfaq/tcfaqA.html -- in other words, a storm over certain areas of water that has thunder and the winds going in a circular pattern. The category includes tropical depressions and tropical storms that have not reached hurricane/typhoon strength as well as the strongest ones.