Seen in its own light this world has never seemed completely real to me and nor have I, as I am, seemed completely real to myself. Now, I definitely don't mean that it is all an illusion. That is not the case. But I would say that both the world and I (and you, of course) are but the outermost parts of something much more substantial. The illusion is to identify this world with the whole world and yourself solely with your outer parts meaning mind as well as body. For instance, I don't think the person called William Wildblood is my whole self. He is real enough but he only represents a limited aspect of the true self. He is the expressed part on Earth of something more fundamental. A few people identify themselves largely with their bodies, many more identify themselves with their minds, their thoughts, desires and so on. But the true self is a spiritual being of which the earthly self is but a projected part, something like a multidimensional thing squeezed into a three-dimensional pot. It is the phenomenal representative of a spiritual being.
Even most people who call themselves spiritual identify themselves with their material selves and worldly personality. They seek to make that better. But this approach can lead to a kind of materialistic spirituality in which the earthly ego is regarded as the one to be saved when in fact it is the earthly ego and its goals and desires that must be put in their place before anyone can be born again in the spirit.
The higher self is our real spiritual being, the central sun, which, as it were, sends down a ray of itself to the physical world in order to gain the experience of life in matter which it needs in order to grow. As the old adage has it, it is separation that leads to completion. You need to break up unity in order to become aware of unity. This earthly representative of the soul in matter consists of mental, emotional and physical parts but with connections to higher levels, principally through the conscience and the imagination, that can be opened up and developed with proper practice and right motivation.
It is probable that the soul on its own level cannot grow or cannot grow in as comprehensive a way as it can in the physical world where it is largely on its own so obliged to develop its mental side and also become a full individual therefore more independent and freer. So we need to leave the spiritual security of the soul to become fully conscious of it and to develop its creative powers. This we do through the earthly personality but that it is more the vessel for our endeavours. It should not be the main focus for them. At the same time, to regard the earthly personality as spiritually irrelevant and as something to be left behind is also wrong. The idea is to combine the two. They are both part of our whole self. Nevertheless it is the soul or higher self that is the centre of our true being. That is the core of our identity.
When the Masters told me that "the greater part of you remains with us" they were referring to the soul. Note that they call it the greater part. They do not call it the real part or the true part. The earthly personality is part of what we are but it is not the whole of what we are.