It's is simply used here to describe a situation, not much different from it's a sunny day. However, what follows is not standard.
You could read it as follows (I put the verses in order):
It's you, it's you must go and I must bide.
It is now like this: it is you that has to go and I will have to stay
and the second verse:
But come ye back when summer's in the meadow,
Or when the valley's hushed and white with snow,
It's I'll be here in sunshine or in shadow,
But if you come back, when it's summer,
Or when the valley is quiet and white with snow,
It will be like this: I will be here (with you) in good or bad times,
So the song describes the current situation, and a promise of a future (possible?) situation, that if the beloved returns, the situation will be different.