You are conscious of your character but are not conscious of your personality. Usually people need cues from other people to tell them how their personality is being perceived.
For example, when you are telling a joke to entertain a group of people, your character knows that you are telling a joke. The delivery of that joke is tied to your personality. When the group laughs at your joke and tells you how funny you are, they are telling you that they perceive your personality to be funny.
At times, a person can behave in a way that can be considered out of character. This usually happens when your personality impulsively reacts to a situation without thinking of how they are being perceived.