Diffusion is when a something moves from a zone of high concentration of that substance to a zone with a lower concentration. There are lots of different ways for diffusion to happen and each has its uses.
Simple diffusion happens when the two zones are separated by a membrane, and the solute can pass through the membrane because it is semipermeable. Over time the solute moves from the area of high solute concentration to the area with low solute concentration.
Facilitated diffusion is when the solute cannot pass through the membrane, so a protein on the membrane essentially opens a doorway to allow the solute to move from the high concentration zone to the low concentration zone.
Active transport is the same situation as facilitated diffusion, but the protein has to use energy to move the solute from an area of low concentration to an area of high concentration. Active transport and facilitated diffusion happen in cells, and allow them to function properly. It plays a major role in cellular respiration during the electron transport chain.
Osmosis is when there is a semipermeable membrane that the solute cannot pass through, but the solvent can, and there is a difference in solute concentration on either side of the membrane. In this case, the solvent moves from the area of low solute concentration to the area of high solute concentration. It can instead be seen as the solvent moving from the area of high solvent concentration to the area of low solvent concentration.
A semipermeable membrane is a membrane that lets some things pass through it but not other things. For example, a phospholipid bilayer is a semipermeable membrane.