When you don't make constant eye contact with the audience, it seems as though you have something better to do or somewhere else you would rather be. Whether you are speaking to an individual or to an audience of two to two hundred, eye contact is that connection that leaves people feeling they are important to you.
When you are speaking, at all costs avoid the "stalker stare." Make eye contact, make the connection and then carry on. In front of a larger audience, don't just stare out to the vast group of people, catch one person's eye while you are saying a few words and then look at another part of the audience, catching another individual's eye. When you finish a topic and are pausing, make sure that the eye contact is maintained at that moment. Starting a new topic gives you that impetus to make contact with another person.
The best feeling is when you are talking and you can see members of the audience nodding their heads and agreeing with you. That is when you have really made the connection. You have drawn them into your circle. You have created the atmosphere of inclusion. Yes, the words you speak are important but without that visual connection, you could, literally, be phoning your presence in.