like what Eventless mentioned, the batteries are lead acid. but without H20, dry acid itself cannot exhibit acidity and hence the use of distilled water which is pure of any contaminants.
sos from wiki.
and to Awakened_Angel, distilled water is NOT for drinking la. since it is so pure, it is very hypotonic. When drank, it will cause excess water entering into our body cells, causing them to burst. Google deplasmolysis or cytolysis.