The reason behind this is that red blood cells are okay when they are in the plasma (the watery part of the blood) because the solutes in plasma are so well balanced that plasma is rendered isotonic. An isotonic solution is a type of solution that has the same salt concentration as its surrounding environment and thus the substances around it e.g. cells neither gain nor lose water. In the blood plasma, the red blood cells neither lose nor gain water and so they remain intact.
However distilled water is hypotonic (has less or no solutes) and therefore osmosis will take place when red blood cell which have a higher solute concentration are placed in it. Water molecules will leave the distilled water and pass into the red blood cells through the semi-permeable membrane of the cells in an attempt to equalize the difference in osmotic pressure on either side of the membrane. In so doing, water will accumulate in the cell which will then swell to capacity and ultimately burst.
