Ions are charged, unbound molecules. De-ionized water is water with the unbound molecules removed, specifically, oxygen and hydrogen molecules. Oxygen is very volatile, will bind with anything, and can cause oxidation.

I had the wife write the above for me, since I also didn't know what de-ionized water was. Wife does research and deals with that stuff.
As far as why I use it for my cigars. I was told by someone that made cigars. "It helps keep them fresh longer and if your trying to rehydrate dried out cigars it'll keep your cigars from cracking." Other then that, it beats me. but I tell others the same as I was told. NOTE: I've never had a problem with my cigars. I'm NOT saying it's due to the water. I do know it's due to alot of TLC though.

Wes