The whole idea of a "social network" is to be social. Be yourself and put your best foot forward. You are the face of your business and your social media presence should be the human side of your brand.
Humanizing your brand is a vast and wide topic that can't be solved completely with a single Twitter account, but you can use social media tools to help get you started.
The first step in humanizing your brand is realizing people are interested in human interactions, not business interactions.
People want to read exciting news that is relevant to them. They want to hear about funny things that you see, hear, and do. People want to hear about the inspiring things you do in your own community. They want to listen to a friend that keeps them "in the know".
To paint a picture for you, imagine that you are out for lunch with a new friend. You talk only about yourself, go on ad nauseam about your accomplishments, credentials, etc. Will you end up being good friends? Probably not.
On the other hand, you discuss your interests, experiences you've had, ask plenty of questions about your new friend, and discover you have much in common.