Everyone here has really good answers, but I just want to add one more point: -"dream away" is used only when someone if awake. When someone is awake and daydreaming, or when someone is thinking about or talking about their goals and hopes for the future, then that person is "dreaming away." For example: "When I told my best friend that I was going to be a famous movie star some day, he told to keep dreaming away. -"dream" is usually used referring to when someone is asleep. When someone is asleep, they can be dreaming or having a dream.

When used intransitively (no direct object), such as "Dream away!", I agree with Su.Ki. More context (surrounding sentences would be nice; this is the ... after your sentence above). Be aware that adding the word "away" after a verb can ALSO have the meaning of "waste". This meaning usually has a direct object. - Throw it away. (discard it; it is trash) - Don't dream your life away. (Don't waste your life by doing nothing but dream all the time. Do some productive, meaningful work!) - I'm going to while away the hours. (waste time doing nothing)

No, you're not saying anything different, but the word 'away' adds something. 'Away' adds the idea of doing this freely, and without worries or constraints. For example, if someone says 'Can I ask you some questions about xx?', you might answer 'Sure. Ask away. Ask anything you like.' So 'dream away' suggests the idea of dreaming happily, dreaming about anything you want and for as long as you want.

Dream away > It's is an idiom ,meaning wasting time having fantasy/dreams in your mind , but not doing anything about it. You can dream away what you want to be in the future . I don't care a bit. Do not dream what you want to be away , ok ?