This is the 5116th most frequent Japanese word.
越
"越" means "to cross over" or "to exceed."
越える is used here to mean 'to cross' or 'to go over', referring to moving past or beyond a geographical feature, the mountain.
山を越えると次の町が見えてきます。
Crossing the mountain, the next town comes into view.
越える is employed figuratively here, describing the action of surpassing or overcoming one's limits or barriers.
彼は自己の限界を越えようと努力しています。
He is striving to overcome his own limitations.
越えて in this context denotes 'passing through' or 'transitioning beyond', illustrating movement through a temporal boundary like changes in seasons.