Osmosis is the movement of a solvent (the liquid that the material is in) into an area with a high solute concentration (the material being dissolved). Osmosis is not to be mistaken with diffusion or the movement of solutes from a high concentration to a low concentration. This diagram illustrates the concept of osmosis across a semipermeable membrane. The source for this picture is rather lengthy but I traced the photo back to a Wikipedia search on osmosis if you care to know the origin of this illustration.
Actually osmosis deals only with water. It involves diffusion of water through a selectively permeable membrane which limits the diffusion of at least some of the solute particles.
Osmosis also means that water will move from a high concentration of water to a lower concentration of water. We use this method to move water around the body as osmosis is passive and requires no energy.
Usually our body uses sodium concentrations to move water around.
Here is a video which explains the changes which occur in red onion cells when they are placed into hypertonic and hypotonic solutions.
Here is a video of a lab conducted to test osmosis in eggs placed into different solutions.
Video from: Noel Pauller