It means simply, "I AM" or "I am that I am". It is a statement of eternality, of independence, consistency, and know-ability. It is also the name God used when fulfilling his covenants with his people (Ex. 3,6).
While I cannot criticize the tradition that has refused to even speak the name, I do feel it goes a little to far. A couple songs capture it's uniqueness, and we'll share one this week and one next.