Preachers are employees who can be hired by the Scholar after constructing a church, dome, or cathedral. They can collect holy water from holy wells, give sermons, and craft items at churches like hosts, parchment, and poems.
Once the church they are hired for has been upgraded to at least a dome, it is possible to purchase the reliquary upgrade which will allow both the scholar and his preachers to 'gain believers', where they go outside the church and preach to crowds. This has the effect of making people more inclined towards your faith, which in turn makes them more likely to attend your church, earning you more money with daily tithes. To use preachers for this purpose, they can be selected from the buildings menu on the right hand side of the screen and sent outside of your dome, and they must be outside before their action menu will show an option for 'gain believers'.
Once you've upgraded to a cathedral and purchased the 'votive image' upgrade, you and your preachers will have an option to 'Pray for God's blessing' when outside of the cathedral. After selecting the action, select one of your buildings and your character or preacher will walk to it, and with a short prayer they will give it divine protection for 24 hours. While this protection is in effect, the building is immune to sabotage.