Order of the Void is a Metaphysics perk that acts as an extra source of faith. You get a percentage of your regular faith income that is automatically "praised" and sent to your Order of the Sun faith pool.
The Void Resonator acts as a buff to time mechanics related to faith income. Normally when you shatter a time crystal and skip a year, the only resource you would gain for your trouble is your yearly antimatter. Resource Retrieval buildings would allow you to get a portion of your other resource income for that year. Void Resonator acts on the same principle, granting you a portion of that automatically praised faith income whenever you skip a year.
Void Resonators would be extremely helpful if, say, you were skipping a whole lot of years to build up a particular resource, and also wanted to build up all your faith bonuses to reach the higher Transcend levels.