Active transport is the final method of how particles move that you need to know.
Surprise, surprise, you should be familiar with your this text-book definition.
Active transport is the movement of particles from an area of low concentration to an area of high concentration. This is against the concentration gradient. This process requires energy.
So basically it is the opposite of diffusion and requires energy.
So where does active transport take place?
Plants need various nutrients to survive, some might move over by diffusion but the plant will want every little molecule it can get. They will move into the root hair cells by being actively transported, using energy.
This is also true in your own gut. Your body will want to absorb as much of the nutrients as possible, so as the concentration decreases in the gut active transport is needed to go against the concentration gradient.