We are beings (souls) who can with the spirit connect to The Divine (this is my own way of referring to the realm of the pure God) and with the body connect to this mortal realm, matter.
The soul is the very essence of who we are; a culmination of our personality, our emotions, our quirks and how we perceive life, tangible and otherwise. The soul has oftentimes been referred to as the incorruptible flesh. It is also sometimes referred to as the mind, although in reality it's a lot more than just the mind. The mind is really how the soul is interpreted to the world around us. Every soul has a purpose of being, whether it is aware of that purpose or not. Nothing in the entire universe, animate or inanimate, is random or purposeless.
The spirit is the very essence of God within us. People tend to say the spirit of this one is with us or the spirit of that one has departed from us. It is actually the souls they are referring to, because upon death the spirit returns to the Essence from which it came. This part of us is all God, possessing full understanding of all things as does God, and knows all things too. Much of this knowledge is of course hidden from our soul, and therefore our existence (our day-to-day lives). But we come into more and more understanding and truth about life as our soul develops during our days in this earthly realm, and as our soul achieves more and more access into the truly immeasurable depths of God. By reason of this, it is our souls that are in various developmental stages, not our spirit; because by virtue of our spirit, we know all, we understand all, and we are all one and the same.
And our days in this realm are only made possible because of the body we possess, also referred to as the flesh. It is the mortal part of our being; which means that it's existence cannot transcend this life. This does not mean that there aren't other beings present with us in this realm. But it definitely means that we who possess body are the only beings whom this realm can really affect in its entirety, since it is with the body that we respond to the various stimuli around us.