Diffusion is the passive process by which molecules move across a semi permeable membrane down their concentration gradient from an area of high concentration to low concentration. An example is gaseous exchange of oxygen and carbon dioxide at the alveolar interface in the lungs.
Active transport is when a molecule or ion needs to be moved against the concentration gradient which requires energy in the form of ATP. An example of this is glucose absorption in the small intestine. Once the glucose has reached a concentration equilibrium with lumen of the small intestine and the bloodstream, active transport is needed to pump the remaining glucose across.