First, it enables customers to have direct conversations with real people inside brands. Secondly, it allows businesses to see what people are saying about their brands in real time, and to respond directly, in real time. Thirdly, it is enabling exciting and weird new ways of communicating.
But is Twitter a brand? Well, it's great branding - great naming system, cute visual identity, and clear what it stands for. But it doesn't yet earn money, emotional attachment is low, and is not as mainstream as many people claim.
Twitter is hugely important, but for reasons that aren't yet clear. Don't experiment with it at your peril.