David wrote this Psalm 3 when his son Absalom rebelled against him and turned the people of Israel against him.  He had to flee Jerusalem with little more than the clothes on his back.  II Samuel 15 says that as he left Jerusalem, David climbed up the Mount of Olives, and he covered his head, and wept.  He bowed his head in weeping and crying and grief.    

So, to “lift one’s head” means that one’s fortunes are restored.  It means that their heads, which were once bowed in sorrow, will then be lifted up in joy. For God to be “the One who lifts up your head” means that He will bring you out of that time of trouble, so that you are no longer bowing your head in misery and pain, because He has lifted your head!