"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.