I think its generally referring to the idea that most people have two sides to their personality (practical and creative) ie you might work in an office but would really rather be a writer/artist. The below should help - the left hemisphere of your brain is thought to be practical (ie doer) while the right is thought to be creative (ie dreamer) - although in your paragraph I think it has it the other way around? The theory is that people are either left-brained or right-brained, meaning that one side of their brain is dominant. If you're mostly analytical and methodical in your thinking, you're said to be left-brained. If you tend to be more creative or artistic, you're thought to be right-brained. And so the dream - he dreams of being a writer but he works as a neurologist. Hope this helps :)

I read it through three times and can't make any sense out of it. The writer uses sentence structures and mixtures of nouns and verbs that I am not familiar with for English composition.