The common belief is that when interacting with someone, you should always make as much eye contact as possible. This is true when you are LISTENING. You would like to appear 100% attentive, so making eye contact with the person is critical. But what about when you are SPEAKING?
When you are speaking, break the eye contact with the listener, from time to time, in order to increase the attention to your words.
If, while you speak, you keep your eyes locked on another person all the time, they will have no choice but to look away to avoid the constant eye contact. This means another object will have caught their attention, even if for only a brief moment. It is at that moment that they are not attentive.
But if you break the eye contact every now and then, the listener begins to make more of an effort to find those moments of eye contact you make with them. To do that, the listener must stay focused on your eyes and thus will be more attentive to everything you say.
You can easily see this work in a group situation. The person speaking makes eye contact periodically with each person in the group, while everyone in the group remains focused on the person speaking. Thus, the listeners make more eye contact with the speaker than the speaker makes with any one listener. The same holds true in a one-to-one situation.
So, when you are doing the talking, periodically break the eye contact and you will increase the attention to your message.