Oh, this one's a doozy. Usually when someone gives their battalion in this format (which is written, in this case, as 6-11 for Army, 6/11 for Marine), it's shorthand -- 6th Battalion, 11th <Branch> <Unit Size>. If he was in WWII, it's entirely possible the designation of the superior unit changed several times over the course of the war, so I wouldn't fixate on that too much. The US army has used about a thousand different designations between all the various regiments styled the 11th (the 11th Armored Cavalry, as they're known today, had at least five different designations in WWII -- and there's also at least an 11th Field Artillery and 11th Infantry, all three being regiments, all three having served in Europe).

Also, it's spelled ordnance. Ordinance usually refers to a law passed by a city or something ("city ordinance"), whereas ordnance (no i) refers to war materiel. It's a subtle little thing and most spellchecks won't pick it up.

Without knowing more about what your great grandfather did during the war, which would help narrow it down, I can really only give broad strokes: an ordnance battalion was essentially a supply battalion, regardless of where it went or what it did (today blowing up IEDs and such is now part of their area of responsibility, but that was less common back in WWII). Since military units tend to use up lots of resources -- like, say, bullets -- they need ordnance battalions to help keep them supplied in the field. Depending on where they serve and what role needs to be filled, they probably won't just be handing out boxes of bullets. They were often the military equivalent of mechanics, responsible for repairing the heavy machinery that enabled them to effectively go to war. So if your great grandfather was in an ordnance battalion in the 11th Armored Cavalry Regiment (to use its modern name, since it had too damned many in WWII), he probably spent time fixing tanks (or maybe not; it's hard to know what he would've done without knowing his "job title," so to speak). Modern ordnance battalions are sort of like general-purpose mechanics and are responsible for fixing everything from power generators to armored vehicles, depending on what unit they are attached to.

This is about all I can do for you without knowing more. But I'm going to recommend you ask at /r/militaryhistory. Those guys managed to turn up some awesome information even when working with very limited information and a fair number of posters there are way, way more qualified to answer this than I am.