The colloquial potential form of 寝る meaning 'to be able to sleep.' Frequently used in spoken Japanese; the standard written form is usually 寝られる.
昨日は疲れてすぐ寝れて、今朝は気持ちよく起きられた。
I was so tired yesterday that I could sleep immediately and woke up feeling good this morning.
試験前で緊張して、なかなか寝れない。
I'm tense before the exam and can't sleep easily.
この薬を飲めば、すぐに寝れると思うよ。
If you take this medicine, I think you'll be able to sleep right away.
赤ちゃんが夜まとめて寝れるようになって助かった。
It was a relief that the baby began to sleep through the night.