“How is he, doctor?”
“Well, he has begun to recover, but he isn’t out of the woods yet.”

“Out of the woods” means “out of danger” or “safe”. In fairy tales, the woods are a scary and dangerous place full of monsters. If someone has taken a step toward safety but is still in danger, we say they are “not out of the woods yet”. The danger can be sickness, enemy attack, failing school, or anything else bad.