Simple Definition:

Osmosis is the movement of water from an area of high concentration [a lot of water] to an area of low concentration [less water] through a semipermeable membrane [a barrier that only allows certain things to pass through].

For example, osmosis can occur when you put a raisin in a glass of water. The water molecules move from an area of high concentration outside of the raisin to an area of low concentration inside the raisin. The raisin swells up and becomes plump as a result.

Very Simple Definition:

Osmosis is when water moves through a special wall that only lets some things go through.