Wide awake with

目(め)が冴(さ)える literally means “the eyes become clear”. It describes becoming wide awake or sharply alert, sometimes so alert that you cannot sleep.

Dictionary Definition

神経(しんけい)が高(たか)ぶって、眠(ねむ)れなくなる。また、眠気(ねむけ)がなくなる。

Unable to sleep due to heightened nerves. Also, to become no longer sleepy.

Goo Dictionary

Further Reading

Examples

Unable to fall asleep after a horror movie with 目が冴える

Manga panel from 好きな子がめがねを忘れた showing example of Unable to fall asleep after a horror movie with 目が冴える.
好きな子がめがねを忘れた » Volume 8 » Page 21

Komura and his mother watch a late-night horror movie. After his mother heads off to bed, Komura texts with Mie from class, who had also watched the movie with her father. The two switch to a phone call, and after a bit the subject of bedtimes comes up. Normally Mie can’t keep awake as late as Komura does.

小村(こむら):
「あ じゃあもう眠(ねむ)い…?」
“Ah, then right now you're sleepy?”
三重(みえ):
「あ 今日(きょう)は… なんか… 目(め)が冴(さ)えちゃって…」
“Ah, today I'm somewhat unable to fall asleep.”