G-man, simply put, is the best model in the multiplayer HL. That's all he really needs to be.
More on topic, however, G-man is some agent from some agency (Assuming government) who watches Gordon's progress. It seems obvious that Gordon is essential to whatever future plans his agency has.
About the speech stutters: I personally, after reading through this and remembering what he sounds like, believe he may be some sort of hologram-like image, perhaps appearing only to Gordon (Tho in HL1 it does look like he is speaking to one of the scientists before the "accident"). It does make some sense. It is by no means the only plausible explanation.