You might be tempted to stop me on this point and mention that Twitter and Facebook are notorious for their ability to garner honest "feedback". That's certainly true, but the signal to noise ratio on those channels is extremely unfavourable. Instead of the constant fire-hose of feedback that you can receive from traditional social media, a customer community allows for a more nuanced approach.
Social media feedback is largely either mono-directional (your customer talks to you, you listen) or bi-directional (you talk back). Customer communities allow for an omnidirectional approach, where you can see your customers interact with each other and join in the conversation as you see fit. The social bonds that you can build with your customers using a customer community also allow you to temper that feedback with knowledge and experience. You know that customer better than a random Twitter username, you can judge better whether their feedback is useful and valid.