Conduction is all about when heat is transferred through a solid. The heat is passed on by vibrations in the molecules. These vibrations get BIGGER when the solid has more. Metals are better conductors than non-metals.
Convection is all about when a gas or liquid (“fluid”) moves and carries heat with it. When the fluid is heated it expands. This means that it will become less dense than the colder fluid around it. Because of this the warmer fluid will try to “rise” over the colder fluid, and this is why warm air rises. This is called a convection current.
When you wear a black t-shirt on a hot, sunny day you would feel hotter than if you wore white. This is because black absorbs infrared radiation (i.e. heat) from the sun better than white does. It also can travel through a vacum. It Can travel through solid liquids and gases.