It also means that they are leaving the garden in terms of - they are embracing free will.
In the garden, Adam and Eve were existing without making their own decisions, but once they bit the apple and learned free will, they had to leave.
It's the same with Aziraphale/Crowley. It's relatively obvious that they've always been able to make their own decisions, but they (and especially their old "sides") have always just seen them(selves) as pawns for their respective sides, with no ability to refuse a directive.
So it's talking about their freedom. They have to make it on their own, now, but also... they *get* to make it on their own. No being forced to the whims of heaven/hell. No more hiding their association with each other. They're free to make decisions about their own lives. It'll be somewhat scary, they only have each other, they're the first of their kinds to embrace it, but it'll be worth it in the end.