According to the Star Wars script, C3PO introduces himself:
I am See-Threepio, human-cyborg relations.
What does he mean, cyborg? Is he claiming to be one?
C3PO didn't want to say about Human and Cyborg relationship because there were other alien species as well as AI-powered robots in Star Wars universe, too.
I think, "Human-Cyborg" is a word similar to "Humanoid Robot" in fashion for thinkable robots to say. We use word Cyborg for a human dependent on machine, but what about a machine dependent on human? C3PO was dependent on human design and architecture to walk etc. So, he was "Human-Cyborg", not "Gungan-Cyborg" or "Besalisks-Cyborg"..
I believe he means he communicates with humans and machines alike. Although it is a rather limited description, since he is fluent in over 6 million forms of communication.
I had always interpreted it as a description of his name and function:
primary function: human-cyborg relations
It had never occurred to me that "human-cyborg" might be his race, but now that it has, I see the line being read as if you were looking him up in an index, which strikes me as a very C3PO-esque way describing himself, as in:
C3PO, odds, calculator of, sharer of, human-cyborg, relations, stiffness of, shininess of, worry-wart