Distilled water is water that's been purified by heating it, collecting the water vapor, then condensing the water vapor back into liquid water - leaving most (perhaps all, depending on the source) impurities behind.
RO water is water that has been passed through a reverse osmosis membrane. Assuming the membrane is functioning properly, it will filter out 95-98% of the impurities. To get the remainder of the impurities out, it can be passed through a deionizing (DI) resin. The water coming out of the DI resin (again, assuming it is not exhausted and is working correctly) will be pretty darn pure, if not 100% pure.
Water that is only passed through an RO membrane is referred to as "RO" water. If it then goes through a DI stage, then it's referred to as "RO/DI".
