Diffusion, Osmosis and Active Transport

Osmosis is just diffusion through a cell membrane.
Diffusion you can read about here.

Active transport is movement across a cell membrane that require the input of energy, usually in the form of ATP. Simple diffusion and osmosis occur passively. Active transport is like pumping water uphill, instead of letting it flow downhill.

ATP is the common energy currency of cells.

Diffusion is a type of passive transport, which means that no energy is spent in the process. A substance move from a higher concentration to a lower concentration. An example of this is oxygen passing through the cellular membrane easily.

Osmosis is still a type of passive transport but this time, the substance is specific and that is water. It is still the same though, water moves from higher concentration to lower concentration until equilibrium is achieved. (Example? I don't think it is still needed).

Finally active transport, here, energy is spent in the form of ATP (usually) to transport a substance. For example, since an ion cannot pass through the membrane easily, it must move through a channel so that it is able to do so. These channels are usually proteins embedded in the plasma membrane of a cell.