To jump over something — to leap across an obstacle or barrier with one's body.
子どもがフェンスを飛び越えるところを大人が止めた。
An adult stopped the child from jumping over the fence.
馬が丸太を軽々と飛び越えた。
The horse easily leapt over the log.
ハードルを飛び越える練習を繰り返した。
I practiced jumping over hurdles repeatedly.
To fly over; to go across through the air (used for something flying across or passing over a distance/area).
飛行機が山脈を飛び越えて遠くの都市へ向かった。
The plane flew over the mountain range toward a distant city.
矢は城壁を飛び越えて城内に落ちた。
The arrow flew over the castle wall and fell inside the castle.
To jump ahead of someone; to skip over (a step or person), e.g. leapfrogging in rank or sequence.
彼は何度も昇進試験に落ちたが、あるとき先輩を飛び越えて管理職になった。
Although he failed promotion exams several times, he eventually leapfrogged over his seniors to become a manager.
本文の一部を飛び越えて次の章に進んだ。
I skipped over part of the text and moved on to the next chapter.