I use Twitter to build relationships with two kinds of people:
1. People who have similar values and a similar vision of making the world a better place. These people share articles, links, blogs, and other info on self-improvement, altruism, leadership skills, spiritual growth, and other related issues.
2. People who have businesses, products, or services that are similar to my own. In my case, I have a book on heroes coming out in the fall, and so every now & then I tweet up the book, or promote my blog on heroes (see my signature for the URL). As a network, we help promote each other's business interests.