This is wise old proverb, the truth of which can never be doubted or underestimated. It simply means that the value of our words can be compared to that of silver, but the value of silence is as precious as that of gold. More than often, we open our mouths to speak and speak what may not be correct and true or sometimes speak more than necessary and even get into trouble. It is important for us to know how and when to speak only what is necessary. We must not utter what is irrelevant and insignificant.
When there is an argument between two people, and both want to make their point, it may be wiser for one to keep silent at that moment, lest a heated argument develops, tempers fray at each other and finally no one really gets out of the problem. But if one keeps silent for that moment, and later, at an opportune moment clarifies his point or clear his stand, it may prove beneficial - perhaps to both persons. The silent one earns the value of 'gold' in the opinion of others.