Diffusion is, on the whole, an effective way to transport essential nutrients into a cell, and take unwanted waste out.
For unicellular organisms like amoebas and algae, this satisfies all of the cellular requirements, but for larger, more complex cells, problems can arise.
The characteristic of a cell which determines how effective diffusion is, is the surface-to-volume ratio. Essentially, a cell with a large surface area will be able to more quickly and efficiently absorb molecules through the membrane than a cell with a small surface area, but both cells may have the same sized volume.
Not the easiest thing to explain. Check out this picture to make it a bit clearer:
