You can devote your dominion to a deity in exchange for some perks (good and bad). For every tick that you remain devoted to a deity, the perks are increased by 0.10% per tick to a maximum of +100%, when the perk values are doubled.
It takes 48 ticks for a devotion to take effect. Your dominion can only be submitted to one deity at a time. However, you can renounce your deity to select a new one (which resets the ticks counter).
The range multiplier is the maximum land size range the deity permits you to interact with, unless recently invaded, and takes effect immediately once you submit to a deity. A dominion with a wider range cannot take actions against a dominion with a more narrow range, unless the two ranges overlap.