Out of difficulties, danger or trouble, as in We're through the worst of the recession—we're out of the woods now, or That pneumonia was serious, but Charles is finally out of the woods. This expression, alluding to having been lost in a forest, dates from Roman times; it was first recorded in English in 1792. The British usage is out of the wood.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.