Plants: Root hair cells lining the surface of plant roots need to move minerals such as magnesium ions from a region of lower concentration (the very dilute solution of minerals in the soil surrounding the roots) to a region of higher concentration (inside the cytoplasm of the cell)
Animals: Food molecules (such as the sugar glucose) can be absorbed across the wall of the small intestine by diffusion, but this is dependent on a concentration gradient existing between the lumen of the intestine and the bloodstream. Active transport allows sugar such as glucose to be transported into the bloodstream from the lumen of the small intestine (the gut) when the concentration of sugar molecules in the blood is higher