We cannot draw a circle without a center point. The Lord is the center, source and essence of our lives. Recognizing Him as the focal point in our lives, we go about doing our daily chores. This is the significance of pradakshina. Also every point on the circumference of a circle is equidistant from the center. This means that wherever or whoever we may be, we are equally close to the Lord. His grace flows towards us without partiality.
Pradakshina done only in a clockwise manner. The reason is not, as a person said, to avoid a traffic jam! As we do pradakshina, the Lord is always on our right. In India the right side symbolizes auspiciousness. So as we circumambulate the sanctum sanctorum we remind ourselves to lead an auspicious life of righteousness, with the Lord who is the indispensable source of help and strength, as our guide - the "right hand".
Indian scriptures enjoin - matrudevo bhava, pitrudevo bhava, acharyadevo bhava. May you consider your parents and teachers as you would the Lord. With this in mind we also do pradakshina around our parents and divine personages.
After the completion of traditional worship (pooja), we customarily do pradakshina around ourselves. In this way we recognize and remember the supreme divinity within us, which alone is idolized in the form of the Lord that we worship outside.