To answer your question simply, yes, investors believe it will be hugely profitable in the future. That's the only reason to invest in any company that doesn't make a profit today.

It is not as unreasonable as you might think. Look at how fast Facebook's earnings are growing in the last 2-3 years. Investors hope Twitter can replicate this, even if it is at a smaller scale. Whether they are right or not is obviously up for debate, and you can take part in this debate by buying/selling/shorting Twitter in the stock market.