My interpretation is that you start to feel comfortable being you.
I would guess that the saying refers to the idea that the body is home to the soul, and that "coming home to yourself" compares to "feeling comfortable in your own skin." The saying also suggests that you view yourself as home and are, therefore, at home everywhere you go. When people are at home they are thought of as being confident, easy-going, dominant... All of these traits would also apply to people who have come home to themselves.
Now that I read your question again, I am thinking you didn't want a definition of "coming home to yourself"... Sorry, I misread.
I spend a lot of my time "detached" from myself. "Coming home" means that I come back to myself to reflect on what I have seen while detached. I explore my emotions, what they mean, what EVERYTHING means.
I think I found the meaning of life once, but my silly INFP brain forgot it..! (Merely kidding!)