The fear of God means different things to a believer and an unbeliever.

For the unbeliever, the fear of God is the fear of the judgment of God and eternal death, which is eternal separation from God (Luke 12:5; Hebrews 10:31). For the believer, the fear of God is something much different.

The believer's fear is reverence of God. Hebrews 12:28-29 is a good description of this:
“Therefore, since we are receiving a kingdom that cannot be shaken, let us be thankful, and so worship God acceptably with reverence and awe, for our ’God is a consuming fire.’”

This reverence and awe is exactly what the fear of God means for Christians. This is the motivating factor for us to surrender to the Creator of the Universe.

Then again, as cited by @stainedsheets, if your ways are not right in God's sight, if you're not keeping His commandments, there's another fear that grows in you, and this time around its called the fear of God due to guit. You feel unworthy, unwhole and no matter your possession, you feel incomplete.