Psalm 40:6-

"Sacrifice and offering you did not desire, but my ears you have pierced (mine hears hast thou opened, KJV); burnt offerings and sin offerings you did not require."

The Psalmist uses this expression to denote that he is a servant of God, ready to do His will.

He is referring to a ceremony by which a Hebrew servant, in desiring to remain with his master, might be bound to him for life:

"If the servant declares, 'I love my master and my wife and children and do not want to go free,' then his master must take him before the judges. He shall take him to the door or the doorpost and pierce his ear with an awl. Then he will be his servant for life." Exodus 21:5,6; see also Deut.15:16,17

This custom was also observed by many other ancient nations.

This psalm is also messianic. Verses from this psalm are quoted in Hebrews 10:5-7, where they are mentioned as being from Christ. This passage magnifies the obedience of the Son that led to His death on the Cross- Phil.2:5-8