It means the condition that heat tries to move outward. So, if you stay next to heater, you can feel warm because the heat of heater comes out.
The sand is hotter in hot summer time, because the sand heated by the sun is hotter and the heat tries to come outward. But, it does not radiate in forest or grass. So, a forest is cooler.

Heat always moves for balancing cold and hot. So, as hot air is going up and cold air is going down, it is called convection.
It is same for metal. For example, there is 1M of a metal stick. If we put the metal stick in cold water and heat it by about 10cm of burner, there is the phenomenon that hot temperature and cold temperature exchange each other for balance in the stick even if we cannot see it. It is called "Convection".

It means the moving speed of heat in the certain object.
Metal has better heat conduction than stone and water and copper, Albata and etc. have much better heat conduction than other metals.
It is the moving speed of heat.