Who or what is the “inner man” Paul wrote about?
The Present State
We are born into sin. The psalmist wrote in Psalm 51:5, “Behold, I was brought forth in iniquity, and in sin did my mother conceive me.” Want more biblical evidence that we are all fallen creatures by nature? The Apostle Paul wrote that “None is righteous, no, not one” (Rom 3:10), and to make it clear that there are no human exceptions, he adds, “All have turned aside; together they have become worthless; no one does good, not even one” (Rom 3:12). I think Paul added “not even one” because there is always that person who thinks they’re the exception, thinking, “I’m a pretty good person,” but no you’re not…and neither am I! The truth is, none are good…not even one in human history, because “all have sinned and fall short of the glory of God” (Rom 3:23). And for the one who is still holding out, thinking they have a “good heart,” Jeremiah writes, “The heart is deceitful above all things, and desperately sick; who can understand it” (Jer 17:9)? We are born into a sinful state…we are living in a sinful state…and we will die in a sinful state, separated from God forever…unless, we trust in Jesus. Otherwise, there is no other hope for us because we all stand guilty before God. 
The Old Nature
If you want to remember the old man or old nature, then look at Galatians 5:19-21 where Paul reminds us that “the works of the flesh are evident: sexual immorality, impurity, sensuality, idolatry, sorcery, enmity, strife, jealousy, fits of anger, rivalries, dissensions, divisions, envy, drunkenness, orgies, and things like these” (Gal 5:21a). Time and again Paul warned them (and us) “that those who do such things will not inherit the kingdom of God” (Gal 5:22b). If someone is claiming to be a believer and still participates in these fleshly things, they are not going to “inherit the kingdom of God.” We might fall into some of these things, but we don’t continue to practice them or do them over and over again. We get up, repent of it, confess it to God, and move on. A Christian might fall into the pigpen like the Prodigal Son did, but if he’s a believer, he won’t stay in the pigpen. A believer will fall into sin…but a non-believer will dive into sin and will swim around in it, enjoying the waters.
The New Creation
After the Spirit of God quickens us to new life in Christ, we become a new creation (2 Cor 5:17). Remember at one time, “you were dead in the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience” (Eph 2:1-2), so we must remember that “we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind” (Eph 2:3), so what changed for us? It was “God, being rich in mercy, because of the great love with which he loved us, even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved” (Eph 2:4-5). We were dead but made alive through the Spirit of God, and now we should produce godly fruit. Such fruit includes “love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control; against such things there is no law” (Gal 5:22-23). It should be obvious to everyone that “those who belong to Christ Jesus have crucified the flesh with its passions and desires” (Gal 5:22-24), since a bad tree cannot produce good fruit any more than a good tree cannot produce bad fruit (Matt 7:18).
The Inner Man
Paul wrote, “I delight in the law of God, in my inner being, but I see in my members another law waging war against the law of my mind and making me captive to the law of sin that dwells in my members” (Rom 7:22-23), so there’s a war going on. We’ll lose some battles and we’ll win some battles, but we must not lose heart because “Though our outer self is wasting away, our inner self is being renewed day by day” (2 Cor 4:16), but our “inner self” or the “inner man” or woman needs all the help they can get. Thankfully, God will “grant you to be strengthened with power through his Spirit in your inner being” (Eph 3:16), so what or who is the “inner man” or “inner woman?” It is that new creation in Christ created by the Spirit of God’s quickening. After we have trusted in Christ, the old man doesn’t give up. He fights us all the way…up until the time we finally enter into glory. The good news is that God sees us as having Jesus’ own righteousness, having become the righteousness of Christ (2 Cor 5:21).
The outer man and woman needs to surrender because he or she is fighting a losing battle. God will bring to glory every child He has saved, but in the meantime, it’s a Battle Royal. We fight an invisible enemy; we fight the flesh; and we fight the pride of life. The inner man must learn to yield to the Spirit of God when prompted by the Spirit of God to do those things desired by the Spirit of God. Even though we’re a new creation in Christ, the old creation doesn’t give up so easily, but even here, we have the unbreakable promise from God that “those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers. And those whom he predestined he also called, and those whom he called he also justified, and those whom he justified he also glorified” (Rom 8:29-30). The older man or woman won’t go away easily, but the new creation in Christ is here to stay…even if they tend to fall back into the old ways from time to time. At least we know, if we fall into the pigpen, the Spirit of God’s coming to clean us up again, and in time, take us to the Father. He is there waiting for us with open arms, ready to embrace us and shower us with kisses. The outer man’s still around, but in time and eternity, he’ll only be a distant memory, so the inner man is here to stay.
Here is some related reading for you: Who or What is the Holy Spirit? A Bible Study 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible: English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.