“For which cause we faint not; but though our outward man perish, yet the inward man is renewed day by day.”  
2 Corinthians 4:16

He informs us of the ‘outward man’; the man everybody can see and relate with and the ‘inward man’ the one that cannot be easily defined by optical observations. The outward and inward man are the same man; put this way- people can easily see your eyes, nose and shake your hands but they can’t read your thoughts or judge your intentions or motivations, those are things only you know about yourself, if you leave the earth by sleeping (death), people can still see that physical you, but the real you- your spirit has vacated that body.
In the main verse, Paul describes what’s happening to his outward man- it’s perishing, and that should ordinarily be a cause for concern, but he says the inward man is renewed day by day, so he emphasizes on the inward man. God wants you more focused inwardly than you are outwardly- if you feed your body good meals everyday, consistent with your exercise routine, wear the best clothes, all of that would not profit you as much as when your spirit is nourished with the word of God, your faith is exercised daily and you put on the whole armour of God. There’s nothing wrong with looking good outwardly, but as you grow in Christ learn to major on what God majors on and minor on what he minors on:
“Whose adorning let it not be that outward adorning of plaiting the hair, and of wearing of gold, or of putting on of apparel; But let it be the hidden man of the heart, in that which is not corruptible, even the ornament of a meek and quiet spirit, which is in the sight of God of great price.” 1 Peter 3:3-4