What does out of the woods mean?

Answer 1

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).

Answer 2

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.