As it pertains to heating, forced convection is a process of conveying heated air into a space. Most commonly in buildings, this is accomplished by blowing air across a finned coil and through a series of ducts which extend from the coil and terminate at grilles in floors, walls, and/or ceilings throughout the building. The coil is typically heated by a furnace, heat pump, or woodstove. Stand-alone units (e.g. space heaters) which simply blow air across a heat source into the adjacent space are also forced convection heaters.
Many of the disadvantages of this method of heating stem from the fact that a large volume of air is required to convey a given amount of heat. Consequently, ducts are rather large and can be intrusive in the building space or difficult to conceal. Insulating them in unconditioned spaces (e.g. attics), can be a pain.
Water is a much better medium to convey heat.