Meaning of "We are such stuff as dreams are made on, and our little life is rounded with a sleep."
Prospero is making an analogy between the spirits, who seem like illusions, to life itself.
The spirits can produce marvelous visions, but when they are done there is nothing left, and not even any sign that they ever were. Rather like a dream... something which can be fanciful or terrifying, but then you wake and it is gone.
Prospero is suggesting that human lives are no different; a sentiment echoed by Hamlet in another work of Shakespeare's. The suggestion is the people live their lives and then are gone, leaving no appreciable mark and eventually not even a memory of their existance. And arguably this may be so - even if we do remember a few figures in history, there are billions more who get no mention; it's even likely that many of the ones we think we remember have little resemblance to the actual figure.
The 'sleep' that rounds life is the sleep of death. An unending nap which gloomy Shakespeare characters often like to say awaits us all.
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我々は夢と同じ物で作られており、我々の儚い命は眠りと共に終わる
http://ja.wikipedia.org/wiki/テンペスト_(シェイクスピア)