Note that greenies as well as most conures have either a flash of color on their head or a solid colored head. It my opinion, it is a way of getting another bird's attention and when he is bobbing his head to you, he wants your attention. Observing Boca and Pichu has really made me understand how important this head bobbing is in their communication. I have started answering their head bobbing with bobbing my fist in response and they get very excited and come to me right after I 'answer' their invitation head bob.
I know very little about conures as my greenies are the first ones I have ever had. But I also have seen cock cockatiels use head bobbing as an attention getting behavior. I started using the fist bobb to answer my tiels and they would bobb back at me and then fly to me. I see the same thing with the greenies. I always wondered why the cock tiels had bright red and yellow patches on their faces and when you see them head bobbing for attention, it becomes very obvious.
I have begun to believe that head bobbing with my greenies is a social greeting and an invitation to interact with them. I haven't read much about wild greenies, but I look forward to reading about their wild behaviors.