Divine Favor (DF for short) represents your relation to your elemental god. If you have enough DF points, your elemental god will grant you blessings at the local temple.
See 'help blessing' for more information about those.
Even though other ways exists, the most common way of gaining DF is to sacrifice things to your god. They accept all valuable objects gladly, but they specially like the hearts of living beings.
These hearts are known to hold elemental powers of the living creature. Every being has divine powers, though most of them are hidden. Only trained priests are able to harness this power. These powers are all in the heart, that's why they are valuable gifts to your god.
To be able to perform the necessary rituals for sacrificing, you have to be at an altar. There are altars all around the Icesus valley, though most of them are located in, or near, the main cities. The power of an altar, and therefore the benefit from sacrificing, varies depending on the holiness of the altar. An altar dedicated to all elements is less powerful as one dedicated to single element, not to mention the main altar of a certain element.
You can find altars dedicated to all elements in some cities, but not all of them. Shrines containing an altar of a single element can be found in the wilderness around the city of Vaerlon. The main altars are located in the main temples scattered across the Icesus valley; One of them, Air, is located inside the city of Vaerlon, others I leave for you to find.