I actually get this question quite often because a modern reader sees the word fear and wonders if it means to be terrified. But that interpretation misses the emphasis of what God is trying to convey when His Word tells us to "fear God."
At its essence, fearing God means to acknowledge and honor the Lord for who He is and to obey His Word. This is what is included in the exhortation to "fear the Lord and shun evil." (Proverbs 3:7)
We have all seen practical examples of this in everyday life while driving on the freeway. People are moving along at a brisk pace until someone spots a police car parked alongside the highway with his radar gun pointed at oncoming traffic. Instantly, brake lights pop on one after the other, as people slow down to avoid being stopped for speeding. Although it may seem somewhat simple, this response to the police officer by those on the freeway is a good example of what it means to fear God. The drivers slow down because they recognize and respect the officer's authority and ability to hold them accountable for their unlawful actions.
When we recognize that God is sovereign and all-powerful and that He has this same authority and ability to hold us accountable for our actions, we respond to Him with what the Bible calls a reverent fear and we adjust our behavior in keeping with His will, whether revealed in His Word or merely confirmed by our conscience.