Here's a great explanation of why we Tweet by the non-profit savvy folks at http://www.givezooks.com
"You are not alone if you are a community based nonprofit and trying to figure out how Twitter can help your organization, but Twitter’s famous simple question, “What are you doing?” is exactly what your supporters want to know. If you focus on that, it may really help you tell your story better than the most highly crafted, polished, committee-approved letter to your constituents.
The question really gets to the heart of communicating the impact that your organization is creating. And impact is exactly what your supporters and potential supporters want to understand about your organization. Supporters want to know how they can help you also, so answering that question on a daily basis, helps supporters understand how they can get involved, promote, spread the work, volunteer, or give. As a community based organization you have the real opportunity to also answer that question of impact in the context of things that might personally affect that follower, their family or their neighborhood. This context helps you make the impact actionable by answering the next question - “How can someone help you make that specific impact”. This is where connection occurs - people can be excited about the impact that your organization is having, but helping your supporters share in creating that impact creates that connection."