There are many different ways to interpret this idea which is found, among other places, in Proverbs 9:10. I would argue that the true meaning of this revolves around what it means to "fear" God.
I would argue that we should think of "fear" in this context as being in awe of God and realizing that God is much greater than we are. We have to realize that God is simply on another level of being, one that we cannot truly comprehend. This is the beginning of wisdom because acknowledging what you do not know (and, in this case, what you cannot know) is the beginning of wisdom.
If you think you know everything on a given subject, you will not be open to learning more about it. This is true about wisdom with regard to our spiritual lives. If we think that we know what life is all about, we are not open to having God tell us the truth. Therefore, we need to admit that our understanding is nothing in comparison to God's. If we cannot understand why God wants us to do something, we need to realize that we are like children who are incapable of understanding why their parents' ideas are right.
So, fear of God is the beginning of wisdom because it allows us to realize that we need to put aside our own attempts to be wise and allow God to guide us.