What does 帮忙 really mean?
Your correct, 帮忙 just means to help (someone). It can also be split apart two word, 幫 as help and 忙 as busy.  

The way the sentence is composed is in a more creative way, that uses the meaning of the characters creatively, both combined and uncombined. However, it's a common technique that shouldn't be over thought.  

你可以幫一個忙嗎? vs 你可以幫忙嗎? are just two different ways of asking if you can help.