The home stack is a way to keep track of where "home" is when you have a lot of temporary moves -- well, it's hard to lose track, but this is just a neat way of thinking about it.
The idea is that the top of the stack is where you currently reside, and when you move, not taking not all of your belongings with you, you push the new residence onto the stack. If you move somewhere (e.g., back) and you take everything with you, you pop the old residence off the stack and push on the new one.
That way, you know that you have some belongings at exactly every residence on the home stack, so you eventually have to go back and get them (that's why they're on the stack -- you have to go back).
It's especially interesting when the residence on the bottom of the stack is the same as the one on the top -- e.g., I grew up born in Maryland, went to college in Pittsburgh, went to work in California for the summer, then visited my home in Maryland for a weekend.
What's the deepest your home stack has ever been?