It doesn't mean you are a little bit joined and a little bit separate. It doesn't mean you can be sort of One but still retain a sense of separate self. It means you are 100%, totally, absolutely, unconditionally, completely the same as, completely equal with, and completely AS ONE with all other people.
In that view, there is actually a whole different ballgame being played which is vastly different to the ballgame of 'duality', which springs up in the ego and makes you perceive others as 'not you'. The only way for you to see yourself as 'separate me' is to distinguish that other people have differences that you do not have, and therefore which prove your inequality, and demonstrate you are not of One mind. It is a huge cover-up.
So in Oneness, the way that you look at a relationship between two people is very different to how you look at relationships with the ego. In Oneness, because you are One, joined, and sharing everything with the WHOLE sonship (not just one individual), everything that you seem to 'do' to other people, or how you view them or perceive them, applies to them, and to everyone else, and to yourself, all at once. There is then no escaping or being able to say, well, I can treat this part of the sonship one way, and I can treat this other part another way, and I can treat myself entirely a third way. In Oneness, everything is shared, there are no private thoughts, and we all access and express the same mind and Identity (Christ 'consciousness').
Another aspect of the Oneness of the Sonship is that, since everything always applies to everyone equally, anything you do applies to everyone and so you can only either separate from everyone simultaneously, or join with everyone simultaneously. If you could visualize that as a vertical ladder, or 'moving vertically' as some people say, to make true progress in awakening you must uncover the sonship's Oneness in 'layers'. So its like you take a blanket off of the entire sonship at once, to reveal a great degree of Oneness that applies to everyone. Or if you choose the ego and you cover things up, you cover up the entire sonship at once with that same blanket. Whatever you apply to one brother applies to all, including yourself.
Now, just because you start applying ACIM or a mindset of Onenss it doesn't mean your mind is fully committed to it right away. It is very conditioned in the ego's 'mind' and a way of perceiving that is very dualistic. Duality basically attempts to fragment the sonship by dividing it up into many parts. Then it says that different rules and values apply to different parts, and that not all parts are the same. This is an attack on Oneness. But we are very steeped in dualistic mindsets and ways of perceiving each other that are very separation-based. Most of the systems in the world are all founded on this idea of separate individuals (as per physical body boundaries). Acting in a body, as a body, leads us to develop a host of distortions and attitudes and perceptual models which are delusional and very blind to Oneness.
So as you start to 'expose' yourself to Oneness, or a thought system of non-duality like with Holy Spirit/ACIM, you gradually start to chisel away at those ways of perceiving and they gradually get 'corrected'. The mind is, effectively, 'healed', because it's belief in separation is a form of suffering. Duality is suffering. So the mind's perception has to be healed so that the way of perceiving dualisti ally can be transformed into a way of perceiving holistically - ie to perceive with Oneness and to see only Oneness.
That takes time. A lot of time. It's a big transformational process. It takes a lot of work and effort and willingness and healing to 'correct' all of the false perceptions and distorted ways of thinking that duality (ego) has assumed are totally normal for a long long time. So usually waking up to Oneness doesn't happen over night. But gradually, slowly, you start to SEE things more from a perspective of Oneness, and with that comes the ability to see things how Jesus sees them - and you realize that ACIM was written FROM a viewpoint of pure and perfect Oneness. Being able to see that makes everything just fall into place and make perfect sense, whereas seeing it through a filter of duality is ... very confusing.
Anyway... Rambling on a bit.. Oneness... as I do unto others I LITERALLY am doing unto myself. As I see others I see myself. I can't wake up and have a happy jolly experience unless I'm willing to allow that experience to include seeing everyone else WITH happiness and joy, and to recognize MYSELF in them. Or more to the point, recognizing that I don't HAVE a self of 'my own' because everyone SHARES IT.