Here, Paul tells Titus how he is to instruct pretty much every aspect of society. He’s already discussed leaders and those who preach an incorrect message in the previous section. Now he discusses old men, old women, young women, young men and slaves.
What’s interesting about this chapter is that it discusses common stereotypes (older, gossiping drunk women; lazy, argumentative slaves), and tells them to counter these stereotypes in how they live. A lot of the ideals mentioned were in fact Greek ideals (being busy at home, for instance), so it’s perhaps a lesson of how we need to be seen as upright not only in a Christian context, but also the context in which we live. Titus was in Crete, a Greek island which had a reputation of being somewhat immoral. Therefore, it was important that the Christians there were an example.
The importance of this is in verse 10 and 11. We are to make the teachings about God attractive so that more may be saved. The grace of God is for everyone, therefore, we should let no one despise us. We were redeemed from wickedness, we are purified and should be eager to do good.