Translation:The child sleeps.
There are actually three ways to translate this sentence using 자다:
아이는 잡니다. = "The child sleeps." or "The child is small."
아이는 잠잡니다. = "The child sleeps."
아이는 잠을 잡니다. = "The child sleeps (the sleep)."
The first one can have an ambiguous meaning due to the homonym formed between 자다 and 잘다. The third one is a reflexive sentence formation that's pretty common in Korean: "you do the thing you do".
Edit: The second one is another common feature in Korean, where verbs are formed by dropping the object particle 을 and merging the syllable blocks together. See 하다 for more formations like this.
From my understanding both are correct and can be used interchangeably, but 는 is more often used when comparing subject with something else in context. If you were just talking about a child, 아이가 works, but if another child was previously mentioned you would use 아이는 because you'd be comparing it to a previously mentioned child. It is a subtle difference, there are videos about it on YouTube.
This is pedantic, but those examples contain the 해라체 (Duolingo: written form) conjugated forms of descriptive verbs. It happens that the written form's present declarative conjugation for descriptive verbs is the dictionary form. Contrast this with the conjugation for active verbs where + ~ㄴ다 is added: 하다 → 한다.
Edit: Note that it is uncommon for the Seoul dialect to use 해라체 in spoken Korean. I believe it is much more common in northern dialects, especially in younger circles.
Also, with 잠 by itself meaning sleep, 잠을 자다 (잠자다) means "to get a full sleep" (like at night).
But you can modify it slightly and get a different meaning. 낮 is daytime, so 낮잠 is a nap. So, 낮잠을 자다 (낮잠자다) means "to take a nap".
Although, you'd likely use the former even for when you work nights and get a "full" sleep during the day.