What is the osmolarity of the body fluids and does it have something to do with osmosis, the diffusion through a membrane?

The osmolarity of our body fluids is about 300 mOsmol/l (seawater about 1000).

Indeed, it has everything to do with osmosis. Every body cell is surrounded by a semipermeable membrane (the plasma membrane) and is therefore subject to osmosis. The body fluids must be in equilibrium with the cell sap. Otherwise, the cells would shrink or swell and die.

The kidneys regulate this by excreting more or less water in the urine. They are, in turn, regulated by a part of the brain (hypothalamus) that contains cells that measure the osmolarity of the blood plasma.