To be clear or vivid (of sight, sound, color); to have sharp, distinct qualities.
秋の夜は空気が冴えて、星がいつもより明るく見える。
Autumn nights are crisp and the stars look brighter than usual.
新しいモニターは色が冴えていて写真がきれいに見える。
The new monitor has vivid colors, so photos look beautiful.
彼は冴えた声でプレゼンテーションを始めた。
He began the presentation in a clear, crisp voice.
To be clear-headed or alert; to have sharp mental focus.
試験中は意外と頭が冴えて、問題がどんどん解けた。
During the exam I was surprisingly clear-headed and solved the problems one after another.
朝ごはんを食べると頭が冴えて仕事がはかどる。
Eating breakfast sharpens the mind and helps work go smoothly.
徹夜明けだが、コーヒーのおかげでなんとか頭が冴えている。
Even after staying up all night, thanks to coffee I can somehow stay alert.
To look lively, cheerful, or perky. (Often contrasted with the negative form 冴えない.)
今日は顔色がよくて、普段より冴えて見えるね。
You look well today — more lively than usual.
冴えない朝だったが、散歩してから少し冴えてきた。
It was a dull morning, but after a walk I felt a bit more lively.
To perform sharply or excellently; to have one's skill or technique at peak form.
投手の球が今日は冴えていて、打者は手も足も出なかった。
The pitcher's pitching was sharp today; the batters couldn't do anything.
彼女はプレゼンで冴えた受け答えをして、聴衆を引き込んだ。
She gave sharp, effective answers in the presentation and drew in the audience.
チェス大会で彼の指し手が冴えていたので、優勝に近づいた。
His moves were sharp at the chess tournament, bringing him closer to victory.
To be strikingly effective or satisfying (somewhat archaic usage).
その一言は場の雰囲気を変えるほど冴えていた（やや古風な表現）。
That remark was so apt it changed the atmosphere (somewhat archaic expression).
作品全体の構成が冴えていて、読む人を引きつける。
The overall structure of the work is strikingly effective and draws the reader in.
To become intensely cold or frigid (archaic meaning; now rare).
夜風が冴えて、外は一段と寒くなった（古めの表現）。
The night wind grew sharp and it became noticeably colder outside (older expression).