What is the difference between diffusion, osmosis and active transport?

Diffusion is the movement of particles, either in gas or solution, from an area of high concentration to an area of low concentration until the concentration in the whole area is equal. This also occurs across permeable membranes. For example, animal cells will build up high levels of carbon dioxide during respiration, whereas the concentration of carbon dioxide outside of the cell will be lower, therefore the carbon dioxide will passively move out of the cell down the concentration gradient. Osmosis is similar, but specifically refers to the diffusion of water from areas of high water potential (dilute solution/very little solutes) to areas of low water potential (concentrated solution/lots of solutes) through semi-permeable membranes. For example, if you put a cell in pure water (water potential of 0), water will passively diffuse into the cell by osmosis because the cell contains lots of solutes (and therefore has a low water potential of 0>).
Active transport is an active process, meaning it requires energy to work. This is because it moves substances against their concentration gradient. An example of this would be plant roots absorbing mineral ions which are in a dilute solution in the soil because they require these minerals for healthy growth.