Answer:
Conduction is the transfer of heat by contact, mostly in solids (metals especially) . In conduction, the molecules of the body in contact with the hot body vibrates about a fixed point. The vibration causes collision between these vibrating molecules and their neighboring molecule, causing them to vibrate too; creating a wave of vibrating molecules that transfer the heat along the solid material.
Convection is the transfer of heat in fluids (liquids and gases), that involves the initial heat transfer between a portion of the fluids molecules and the hot body (conduction) at the thermal boundary, and then the eventual movement of that portion of the fluid from that position to a colder part of the fluid. The heated fluid is replaced by a colder fluid (this is due to buoyant forces due to difference in density of the cold and the warm parts of the fluid). This movement ensure thorough mixing of the fluid and the eventual heating up of the entire fluid.
From the above statements one can clearly see that convection is comprised of an initial heat transfer by conduction at the thermal boundary, followed by movement of the fluid molecules.