Heat transfer by conduction occurs because particles in a solid can vibrate. When a source of heat is applied to an object, the energy is transferred to the particles in the solid, making them vibrate faster. This causes the nearby particles to vibrate also, and the energy gets passed right through the object. But none of the particles actually move through the solid. 
  Heat transfer by convection happens in a liquid or gas, where particles gain heat, and move around faster. Because they are not locked in place like in a solid, they can move around ... taking the heat energy with them.
Heat transfer by radiation involves some hot object which is able to give off energy in the form of electromagnetic radiation, such as a hot filament in a light bulb. The energy that is given off travels at the speed of light, and does not require a medium to travel through. 
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