Diffusion is a transport mechanism (another example of a transport mechanism is advection) in which the material moves from a region of higher concentration to a region of lower concentration. Think of a cube of sugar in a glass of hot water. The sugar moves from the cube (a region of higher concentration) to hot water (a region of low concentration of sugar).
Diffusion is very important for living organisms as it is essential for intake of useful materials and removal of waste materials. For example, oxygen is needed for our bodily functions, while carbon dioxide needs to be removed from our body. Fresh oxygen diffuses into our (oxygen-depleted) blood, while carbon dioxide is diffused out from (carbon dioxide rich) blood. This process also helps limit the loss of body heat to the environment.
Hope this helps.