Credibility and believability are important when you plan to reach others with a message of any kind or import.   When you communicate with others even on a one-to-one basis your personal credibility adds weight to what you have to say.

Your truthfulness is only part of the equation.   Your passion and dedication to your beliefs are important as well.   Keep in mind that consistency is a positive message.   If you have an on-going relationship with an individual or audience then they have formed expectations of you and your ideas.   Any time you deviate from ideas or behaviours, your credibility will be questioned in the minds of your listeners.   Thus always examine your utterances to be sure they are not inconsistent or frivolous.   We are not talking about conversations where ideas are exchanged and you might tend to "trot out" new ideas or theories for friends or associates to consider and provide you with feedback or alternate ideas or critical insights.   It is only when you have run your ideas through these "filters" that you should consider exposing them to others in speeches or even casual conversations.   "Shooting from the lip" has never been helpful in establishing or maintaining your personal or professional credibility.   What you have to say has far more weight with others than you might think.

The measure of you as a person is dependant on in a great degree on your utterances.   Body language while you are speaking also influence how your communication is received by others.   As a professional person you must always strive for excellence in all you do so just to be adequate in your personal communications is not acceptable.