for the new deity system see here
A Tithe is a sacrifice of items at an altar to your god. A sacrifice carries the benefit of small gains to favor points.
Only specific items may be sacrificed at an altar. In general, "treasured" or greater items that are dropped by mobs or in chests, which have no stack size are able to be sacrificed. Items that are master-crafted are also able to be sacrificed.
Common craft items and items that are stackable are usually not allowed to be sacrificed, as well as quest items and special-use items.
At a sacrificial altar to your god (usually placed in your room), there is a box at the bottom of the altar's use window. Placing an item in this box will either yield a favor amount or the message "[Your God] would be displeased with this offering." Those with favor listed are able to be sacrificed.