Even so ye also outwardly appear righteous unto men, but within ye are full of hypocrisy and iniquity.
This is a classic problem among people trying to be religious: fasting, getting baptized, trying to get into a better situation in this world. People try to make themselves right by making things seem right on the outside, or on the outward appearance of things.
Many people even have this problem in the question of salvation and the salvation message. The popular gospel is that, People could have been saved if they kept the 10 commandments, and that Now people can be saved by believing and repenting from their sin (and sometimes making Jesus the Lord of their life,) but not just by believing. True belief,
The New Gospel says, not only results in a change of action, but consists of a change in action on the part of the saved.
That false gospel is a gospel of salvation by works, because turning away from doing sin, improving one's outward actions, and making the Lord into the master of every area of one's life is good works.
The unpopular, age-old, true gospel, says, that being saved is not by anything good that we can do, but only by belief in our hearts in the Lord Jesus Christ, and the free gift of the good things that He has done for us. We need to stop trying to make ourselves right by improving the outward appearance of our lives, and do things the right way. Have an honest change in the thoughts and intentions of our hearts, a change in what we believe and what we desire. Inner change will naturally translate into outward improvement, not the other way around.
And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem.
This teaches that repentance is one of the things that we're supposed to preach in Jesus' name... But repentance in what way?
I think that we should preach for people who don't know Jesus to repent in their hearts from their unbelief, so they can be saved by believing in the Lord Jesus Christ. I think we should preach for believers to turn from what unbelief in Him they might still have. I also think we should preach for believers to repent from wrong-doing, so they can walk with the Lord in a way that's worthy of the salvation we've received.
Of course, it would be great if people who don't know Jesus would turn from sin too. However, telling unbelievers to stop sinning is not the gospel. We can't really stop without His help. Even if we could, it wouldn't do us any good because we can't save ourselves. The most important thing we need is to believe in Him. Only by believing in Him can we be saved in the first place, and only by believing in Him can we really repent from our sins.