So, there's one of two ways a born-again person lives every day:
1.) In the power of their flesh (intellect, determination, physical strength).
2.) In the power of the Holy Spirit.
More often than not, at least in my experience, Christians are working to achieve a godly life from the first power source while assuming they're doing so from the second. This is a spiritual catastrophe. Paul explained why in various of his letters:
Romans 7:18-19
18 For I know that nothing good dwells in me, that is, in my flesh; for the willing is present in me, but the doing of the good is not.
19 For the good that I want, I do not do, but I practice the very evil that I do not want.
Romans 8:5-8
5 For those who are according to the flesh set their minds on the things of the flesh, but those who are according to the Spirit, the things of the Spirit.
6 For the mind set on the flesh is death, but the mind set on the Spirit is life and peace,
7 because the mind set on the flesh is hostile toward God; for it does not subject itself to the law of God, for it is not even able to do so,
8 and those who are in the flesh cannot please God.
Galatians 5:17
17 For the flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please.
Galatians 6:7-8
7 Do not be deceived, God is not mocked; for whatever a man sows, this he will also reap.
8 For the one who sows to his own flesh will from the flesh reap corruption...
And so on.
To work to accomplish a supernatural effect (Christlikeness - Ro. 8:29) by natural, fleshly power is to make failure certain. Like begets like: A duck begets a duck, a cat begets a cat, a dog begets a dog and the flesh only begets the flesh. According to God's word, the only thing the flesh, by itself, can produce in you is spiritual and moral corruption, destruction and death (See above and: Ga. 5:19-21).
Why, then, do so many believers rely upon their flesh (intellect, determination, physical strength) to achieve godliness? Well, how else do we live except in the flesh? We exist in "tents" of flesh; we preach, teach, love, and serve with our physical bodies, so there's no getting away from the flesh in Christian living. What does it mean, then, to walk in the power of the Holy Spirit rather than in the power of the flesh?
The main difference is that the one "walking in the (power of the) Spirit" does so under the Spirit's constant control. In his letter to the Galatian believers and to the believers at Rome, Paul indicated that being "led of the Spirit" was a chief characteristic of being Spirit-minded and of "walking in the Spirit" (Ro. 8:13-14; Ga. 5:16-18). Being "led of the Spirit," as Paul explained in Galatians 5:25, is "walking in step" with the Spirit, which is much more than his merely influencing the Christian's living. This is made clear in the following:
Romans 6:13
13 and do not go on presenting the members of your body to sin as instruments of unrighteousness; but present yourselves to God as those alive from the dead, and your members as instruments of righteousness to God.
Romans 6:19
19 I am speaking in human terms because of the weakness of your flesh. For just as you presented your members as slaves to impurity and to lawlessness, resulting in further lawlessness, so now present your members as slaves to righteousness, resulting in sanctification.
Here, Paul taught that born-again people are to present themselves ("yield themselves" in the KJV) to God as His "slave of righteousness." Paul is not proposing that the Spirit merely suggests, and prods, and tickles the believer's mind and conscience in a godly direction but that they submit to the rule of the Spirit as a slave to their Master. Doing so, Paul writes, "results in sanctification."
Romans 12:1
1 Therefore I urge you, brethren, by the mercies of God, to present your bodies a living and holy sacrifice, acceptable to God, which is your spiritual service of worship.
What does yielding, or presenting, oneself to God as His slave mean? Here, Paul explains: Be a living sacrifice to God. The Spirit doesn't merely guide, or assist, or support the born-again believer, but requires that they yield themselves to His will across-the-board, forsaking all personal rights and autonomy.
"A living sacrifice. A sacrifice is an offering made to God as an atonement for sin; or any offering made to him and his service as an expression of thanksgiving or homage. It implies, that he who offers it presents it entirely, releases all claim or right to it, and leaves it to be disposed of for the honour of God. In the case of an animal, it was slain, and the blood offered; in the case of any other offering, as the firstfruits, etc., it was set apart to the service of God; and he who offered it released all claim on it, and submitted it to God, to be disposed of at his will. This is the offering which the apostle entreats the Romans to make; to devote themselves to God, as if they had no longer any claim on themselves; to be disposed of by him; to suffer and bear all that he might appoint; and to promote his honour in any way which he might command. This is the nature of true religion."
- Barnes' Notes on the New Testament.
There can be no "walking in the Spirit" apart from this radical submission to God (Ja. 4:7, 10; 1 Pe. 5:5-6) in everything. And if there is no "walking in the Spirit," there can be no true victory over the flesh (Ga. 5:16). One must be consciously, explicitly submitted to God, as Christ demonstrated for us in Gethsemane; to be otherwise is to be a rebel toward God. And if a believer is a rebel toward God, however pious their living, they will not be filled with power of God that is necessary to the supernatural transformation He wants to work in them. In such a condition, the believer will resort to their own human, fleshly power in an attempt to "work out their salvation" and produce a fleshly counterfeit of "life in the Spirit."