When the cell needs a nutrient, molecules of that nutrient have to pass through the cell membrane and get to the center of the cell. When the cell is bigger (more volume), the center of the cell is further away from the membrane, and that makes more difficult for the cell to use the nutrients that have got in. When the cell is longer (more area), there is more membrane, so the molecules have more possible places from which they can get inside the cell. So this process is easier when the cells are long and small, which is when the rate Area/Volume is very small. You can compare this with cooking a hamburger: if it's too thick, it may end with a raw center and a burned surface - that's because the heat is having some issues getting to the center of the hamburger.
