Translation:저는 노래를 합니다.
with the verb conjugated into the polite form, it would be "저는 노래해요."
Without it, the sentence would just be "I song", which isn't right in English or Korean grammar. You can say 저는 노래합니다, "I sing", or 저는 노래를 합니다, "I do the song", or even 저는 노래를 노래합니다, "I sing a song". But there needs to be a verb or the sentence doesn't work.
In this sentence, 노래 is behaving as a noun (it has the object marker, 를), so 합니다 is required to complete the sentence.
합니다 is formal expression of 하다.
To sing is 노래하다 or 노래부르다 in Korean.
노래하다 is 노래+하다.
(Do a song? I don't know that expression is in English haha)
Some noun with -하다 can be verbs like 노래하다. I think 말하다(to speak) can be another example. 말하다 = 말(word, tongue) +하다 = to speak
Why they put 를 cuz its not complement, its a verbe so dont need this... and why its 노래and not 부러요 ?
This course is designed for English speakers who don't know any Korean. At this point 노래 is the only word we've learned for "song"; given as how 노래 is a noun (the verb form is 노래하다), it makes sense it gets marked as such in this context.