Read: Proverbs 9:1-12 and Luke 1:46-56
The fear of the Lord is the beginning of wisdom, and the knowledge of the Holy One is insight. (Proverbs 9:10 ESV)
And his mercy is for those who fear him from generation to generation. (Luke 1:50 ESV)
At her incredibly young age I'm not sure that Mary completely understood the ramifications of God's plan for her life. I'm not sure she fully grasped the scope who Jesus would be, yet she fully embraced God's plan. The biblical author Luke records a word of praise she offered up to God prior to Jesus' birth. It is a beautiful song full of meaning. One of the key parts is Mary's acknowledgement of her fear of God.
Some fears are entirely irrational. They seem to come from nowhere for no reason, and produce nothing positive. They are inhibiting or deconstructive in nature. Not so with Mary, or anyone else who displays a healthy fear of God.
We usually classify fear as something that either paralyzes or goads us into action. We think of it as the condition or onset of being scared. But the kind of fear that the Bible classifies as healthy is altogether different. It is not synonymous with terror. It is more akin to reverence. Fear of The Lord does not mean to harbor an irrational terror before God. To have the fear of The Lord is to approach God through the grace of Jesus, with reverence. Reverence is a holy kind of fear. It is a rational reaction to the unfathomable majesty of God contrasted to our own meager being.
Mary demonstrated this well. Jesus, the Son of God, demonstrated it as well. It means being able to go to God in fear without being afraid.