You shall fear the LORD your God; you shall serve Him and cling to Him, and you shall swear by His name. (Deuteronomy 10:20)
The literal commandment is that we should fear (have reverent awe for) the LORD our G-d.
Messiah affirms this commandment when He warns His disciples against hypocrisy.
But I will warn you whom to fear: fear the One who, after He has killed, has authority to cast into hell; yes, I tell you, fear Him! (Luke 12:5)
Messiah had a reverent awe of His Father and constantly sought His Father's glory (John 12:28).
As the only Begotten Son, Messiah knew that He was subordinate to the Father and constantly walked in reverent awe of Him and submitted Himself to the Father's will (Philippians 2:8).
Traditional observance of this commandment is focused on the manner in which a person obeys G-d's laws. A son, when instructed to mow the lawn, can do so petulantly and reluctantly but the manner in which he responds to the instruction does not reflect reverence towards the father who gave the instruction.
We are able to fulfill this commandment today and we, too, should fear G-d reverently.
The reverent fear or awe we should have of G-d is not abject terror that would cause us to cower under our beds (unless a person knows they are in sin and has not been redeemed by the blood of the Lamb!). It also should not be a false, fawning, obsequious fear [imagine Eddie Haskell from Leave it to Beaver].
The reverent fear of the Lord one should exhibit is one that should be born from genuinely knowing that they are serving the Creator and Sovereign King of the universe.