Okay, first off, the word "no-self", Rosemary and I don't usually use that word. "Not self" is slightly different, which Rosemary explained a few days ago. But at any rate, what is it that cycles around in various lives. Buddhism says that it is a changing entity that moves from one life to another. Cycling around in lives. But there's a changing entity. What was born into my body, the consciousness that moved into my body, joined with egg and the sperm of my parents. Then evolved and grew due to nutrition, food and everything. Then teaching and friends and family affected me into who I am now. The being who was born, it was a consciousness that came and joined the material aspects, the fetus. When I die, it's my consciousness again that moves to a new body. But this consciousness moving to a new body, will be the consciousness of me when I die, which is different to the consciousness of who I was when I was born.
So it's a changed identity, it's not the same identity. It grew out of that consciousness. Who I am now grew out of that consciousness. But all of my "makeup", my Kamma, my understanding, all of my wisdom, my compassion, everything, is of a different quality to what it was when I was born. When I die, hopefully I'll be much more improved. So then my rebirth takes hold with a new type of consciousness, new type of Kammic "makeup", which then creates a new being. So the "it", is basically our consciousness along with our Kama. As to which way we're going to go: good Kamma brings us a good rebirth, bad Kamma brings us a rebirth that is not so good.
Now, I will mention, this is the theory part of Buddhism. Once again, this is the theory part of Buddhism, it's not something I can prove, I don't know it for a fact. This is how I interpret what I've been taught and read.