When red blood cells are placed in distilled water, which is hypotonic compared to the solution contained within the cells' membranes, the distilled water will diffuse into the red blood cells and cause them to burst. Placing red blood cells in any solution which contains a lesser degree of solute than that of the solution within the cells will cause water to diffuse into them. Because distilled water contains a zero concentration of solute, it will predictably diffuse into a red blood cell in an attempt to equalize the osmotic pressure on both sides of the cell membrane.
In a healthy organism, red blood cells are able to maintain their shape, and neither expand nor burst within the bloodstream, because the osmotic pressure within the cell is equal to the osmotic pressure of the blood serum surrounding it. This balance of osmotic pressure is referred to as isotonicity. If the serum in the bloodstream were to contain a lesser concentration of solute than the solution within the red blood cells, this would make the serum hypotonic. The unequal osmotic pressure would then cause the water portion of the blood serum to diffuse into the red blood cells, causing them to swell.