Osmosis is when water particles move from an area of high concentration (or a crowded area) to an area of low concentration (or a less crowded area). This is a process that happens inside a cell. It is very important because most of the cells fluids are water. When particles travel inside the cell, they go through a semipermeable membrane, which lets some particles in and only some out.
Equilibrium occurs when no overall change appears to take place.Using the example of evaporation: In a closed container molecules of water will evaporate from the surface of the liquid until eventually no more vapor molecules can enter the air space. That does not mean that the molecules of water are no longer evaporating. They haven't called a meeting and said that's it we won't do this anymore. It means that the rate of evaporation of molecules is the same as the return of molecules to the surface. We could get more molecules into the air by increasing the temperature but eventually the rate of evaporation is the same as the rate of condensation.Exactly the same with diffusion and osmosis. Molecules will diffuse into an area of lower concentration until the concentrations are the same. This does not mean that the molecules/particles then go to sleep. The particles are diffusing equally in each direction so the overall diffusion is at equilibrium.With osmosis, the particles diffuse across a semi permeable membrane until the concentration is the same on both sides. The particles then will diffuse in each direction at the same rate - equilibrium has been reached.