Osmosis is the movement of water molecules from an area of high water concentration to an area of low water concentration through a partially permeable membrane.
Osmosis is a type of diffusion, so when there's a different water concentration the substances move. The "things" (usually cells) will then increase in size because there are more substances in it.
What is osmosis and why does osmosis make things increase or decrease in size ?
Concentration of solutes in your body cells need to be kept constant for them to work properly. However, if the concentration of the solutions outside your cells may be very different to the concentration inside them and therefore the concentration gradient move into or out of the cells by osmosis.
Then you can go on and talking about the effects osmosis has on animal cells (isotonic, hypertonic and hypotonic)
Water does have a molar concentration, so it might be accurate to refer to "water concentrations", but I fear this might confuse things, because in reality water actually moves from a low SOLUTE concentration to a high SOLUTE concentration, so there is potential for things to get mixed up if you say that osmosis is water moving from a high water concentration to a low water concentration..
As for changes in size, well, if you think of a cell as a water balloon for example, then anything that is going to increase the solute concentration inside the cell relative to the outside is going to draw water into the cell by osmosis, causing the cell to expand like a balloon. Similarly, anything that is going to decrease the solute concentration inside the cell relative to the outside is going to draw water out of the cell. For example, if you were to start peeing a lot, e.g. in diabetes, then you're losing a lot of water from the body, this is going to raise the concentration of salt in the extracellular fluid, and so you start drawing water out of the cells.
Hope that makes sense