"On my way home" refers to anything that you do while you're coming home from somewhere, like from work, from a vacation, from shopping, etc.
The phrase "on my way ___" is usually followed by "to ___":
I was on my way to work when she called.
But "home" is special because you never use "to" with it:
I'm going to Ted's house.
I'm going home.
"Here" and "there" are also special in the same way:
He's on his way here right now.