1To cross over or pass through — to move past a place, boundary, or period to the other side. Used for physical features like mountains, rivers, and borders, as well as time markers (years, periods) understood as 'crossing over' to the next phase. Also covers figurative uses like overcoming a difficulty. The kanji 越える is preferred for this sense.
国境を越えるにはパスポートが必要だ。
You need a passport to cross the border.
峠を越えると、急に視界が開けた。
Once we crossed the mountain pass, the view suddenly opened up.
厳しい冬を越えて、ようやく春が来た。
We got through a harsh winter, and spring has finally arrived.
彼は数々の困難を越えて、ついに夢を実現した。
He overcame many difficulties and finally realized his dream.
2To exceed or surpass — to go above a quantity, level, or standard. Used for numerical or qualitative thresholds: 100人を超える (exceeding 100 people), 予想を超える (surpassing expectations), 限界を超える (exceeding one's limits). The kanji 超える is conventionally used for this sense (越える is occasionally seen but is non-standard for this meaning).
今年の参加者は予想を大きく超え、500人に達した。
This year's attendance far exceeded expectations, reaching 500 people.
この映画は公開二週間で興行収入が十億円を超えた。
This film's box office exceeded one billion yen within two weeks of release.
練習で自分の限界を超えるのは簡単ではない。
Pushing yourself past your own limits in practice isn't easy.
彼の演技は私たちの想像をはるかに超えていた。
His performance went far beyond what we had imagined.
気温が35度を超える日が続いている。
Days with temperatures above 35°C have continued.