To the best of my knowledge the sentence is usually written in the negative form, ex.: "we are not out of the woods yet", that is we are not safe yet, we did not solve all urgent issues/problems yet (but implying you are getting there).
This is an idiom meaning that the danger is past, as though you were traveling through a deep forest, but you have come out on the other side now.
chase someone in the woods
Penns Woods.
Tiger Woods
bear in woods
Penn's woods.
to camp in the woods.
to be camofloudged
in the woods
woods
A neck is a thin area, as in a part of the woods. "In your neck of the woods" just means where you are, in your part of the world.
Penn's woods.
It means "the woods."