1Crossing (a road, river, etc.); traversing or cutting across a space (often used for walking/going across).
歩行者は横断歩道を渡った。
The pedestrian crossed at the crosswalk.
道路を横断する前に左右をよく確認してください。
Please look both ways carefully before crossing the road.
川を横断するために橋を渡った。
We crossed the bridge to get across the river.
2Crossing in an east–west sense; traversing or traveling across a large area (e.g., flying or sailing across an ocean or country).
彼は自転車で日本列島を横断した。
He cycled across the Japanese archipelago.
飛行機が太平洋を横断した。
The plane flew across the Pacific.
その道路は市内を東西に横断している。
That road runs east–west across the city.
3Cutting horizontally; taking a lateral cross-section (e.g., in anatomy). In modern usage, it's also commonly used figuratively (as 横断的) to mean spanning or cutting across multiple fields, departments, or organizations.
この問題は部署を横断的に解決する必要がある。
This problem needs to be solved in a cross-departmental way.
その研究はいくつかの分野を横断的に調査したものだ。
That research investigated several fields in a cross-disciplinary way.