This is the 4093rd most frequent Korean word.
잠이
"잠이" means "sleep" or "sleepiness" in English.
잠이 here refers to the state of sleep, and using '오지 않아서' indicates the inability to enter the state of sleep.
잠이 오지 않아서 책을 읽었어요.
I couldn't fall asleep, so I read a book.
잠이 in this context represents the general amount or tendency toward sleep one has.
그는 잠이 많아서 아침마다 일어나기 힘들어해요.
He sleeps a lot, so he struggles to wake up every morning.
In this sentence, 잠이 characterizes the depth or quality of sleep experienced.