To pass the peak/difficultest part of something; to get through the worst (e.g., of an illness or crisis). An idiomatic expression.
患者は峠を越したと言われ、家族は少し安堵した。
They said the patient had passed the worst, and the family felt a bit relieved.
プロジェクトはようやく峠を越したので、残りは細かい調整だ。
The project has finally gotten past the hardest part, so the rest is fine-tuning.
震災からの復興も徐々に峠を越しつつある。
Recovery from the earthquake is gradually getting past its most difficult phase.
To cross a mountain pass; the literal meaning of traversing a ridge or pass.
朝早く出発して峠を越し、隣の村まで歩いた。
We set out early in the morning, crossed the pass, and walked to the neighboring village.
昔の旅人は馬で峠を越すのが普通だった。
In the past, travelers commonly crossed mountain passes by horse.