If granted, it would allow networks to extort, essentially, payment from any web site, to make sure their service is accessible by its users.
This article is a good summary of what's at stake: http://www.washingtonpost.com/wp-dyn/content/article/2006/06...
A non-neutral network is one possible outcome of an inefficient oligopoly structure of the high-speed internet connection market. If we want to avoid that inefficiency it behooves us to at least threaten regulation of the market. Hopefully the threat will be enough but if not then regulation becomes more of a requirement if one is concerned with economic efficiency.
Remember the POTS network was built-out using a government-sponsored monopoly (AT&T). If such an unwieldily structure could bring copper wires out to every rural farmhouse in the country surely the "free market" will be able to provide high-speed internet connections just as universally without having to resort to inefficient extortion of high-tech companies.