Learn Turkish: Çocuğun sesi çok güzel. - The child's voice is very beautiful.

When a Turkish word ends in k and gets a suffix starting with a vowel, the k usually softens into a ğ (soft g). Here, we are adding the genitive (owner) suffix -un to çocuk to make it mean "the child's". Because -un starts with a vowel, çocuk + -un becomes çocuğun.

What does the -i at the end of sesi do?

It is the possessive suffix meaning "his/her/its". In Turkish, to make a definite noun compound (like "the child's voice"), you don't just mark the owner. You also have to mark the thing being owned. So ses (voice) takes the -i suffix to complete the pair, giving us çocuğun sesi.

Could I just say çocuk sesi instead of çocuğun sesi?

You could, but it would change the meaning! Çocuğun sesi uses the owner suffix on the first word to show we mean a specific child's voice. If you say çocuk sesi (without the owner suffix on the first word), it becomes a general category meaning "a child's voice" in general, rather than the voice of the specific child you are looking at.

Where is the word for "is" in this sentence?