Diffusion is an equalling of the concentration of particles within a given unit of space. A good example of diffusion would be if I strike a match in one corner of the room, in just a few minutes, the odor of sulfur from the burning match would spread throughout all the air molecules within the room.
Osmosis is a form of diffusion, except through water concentration within an object. It is a process which equallizes the water content in an organism or unit by passing water across a semi-permeable membrane, which means the membrane will allow some things to pass through, but not all things. A good example I used in my class room this year to demonstrate osmosis was to take an egg and soak it in vinegar for 24 hours to remove the calcium from the egg shell. The next day, I took the now pliable egg and immersed it in table syrup, which has a low concentration of water, for another 24 hours. The next day, I removed the egg, which was now "deflated" because some of the water content within the egg diffused across the membrane into the syrup, in an attempt to equalize the water concentration. I then took the "delated" egg and soaked it another 24 hours in water; the next day, it was back to it's original inflated self, as the water diffused back into the egg.