Diffusion occurs when there is a unbalanced concentration of a solute in a solvent. The solvent will naturally move through random motion of its particles (Brownian motion) until the solute is uniformly distributed throughout the solvent. This process of a solvent moving from a location of extremely low concentration into an area of higher concentrating of solute in order to equalize the concentration is diffusion.
If the highly concentrated solute is separated from an area of highly concentrated solvent (or low solute concentration) by an impervious membrane the diffusion will be blocked. However, there are some membranes that will allow certain types of material through them and yet block others. Membranes of this type are called semipermeable. A good analogy for a semipermeable membrane would be the screen on a window: the screen lets some thing through (air and light) but blocks others (bugs).
If the semipermeable membrane allows only water to pass through it, and the solvent in a solution is water then water will move through the membrane from a place of high water (low solute) concentration into an area of high solute concentration. The result will be that the water will pass through the membrane and dilute the solute.
Osmosis, then, is the transfer of water through a semipermeable membrane from an area of high water concentration into an area of high solute concentration.