The Anglo-Saxon word "god" means "good" and is equated with divine goodness or holiness. I've read that ic/ith means "war", but I haven't found anything so far that is conclusive on this. It seems feasible that "holy war" is accurate, but like so many things on the internet, I would not consider it fact without finding definite meanings of the root words.
ETA: This intrigued me (as I'm a sucker for Anglo-Saxon names), so I did some more digging. I checked the database for other names containing "ith" and I did find the Old English gyð meaning "war/battle". According to http://www.s-gabriel.org/names/talan/reaney/reaney.cgi?Godith Godith comes from Godgýð. If this is true, it would indeed mean "holy war".
"It's the job that is never started that takes the longest to finish." - J.R.R. Tolkien