To wake up (from sleep); to open one's eyes and become awake.
毎朝六時に目を覚ます習慣がついた。
I've gotten into the habit of waking up at six every morning.
彼は寝過ごさないように、アラームで目を覚ます。
He uses an alarm to wake up so he doesn't oversleep.
目をさますと、窓の外はもう明るくなっていた。
When I woke up, it was already light outside the window.
To sober up; to come to one's senses; to become enlightened or realize the truth (figurative uses).
彼は酒に酔っていたが、時間が経って目を覚ました。
He was drunk, but after some time he sobered up.
厳しい現実に直面して、ようやく目を覚ましたようだ。
Facing harsh reality, he finally seemed to come to his senses.
その事件がきっかけで、彼女は人生観が変わり目を覚ました。
That incident was the trigger; she changed her outlook on life and was enlightened.