The Cathedral is located in the Capital portion of the Skyforge menu. Primarily a method for increasing Might, the Cathedral allows you to host Rituals that can increase your number of followers. Also, your followers will provide you with daily gifts upon visiting the Cathedral.
From the Skyforge Update containing the Cathedral:
"Now mortals from all around Aelion will visit your wonderful Cathedral. And the more that come, the higher your might will be! But don't expect the number of cult followers to grow just like that — the planet has a lot of gods and you need to show people why they need to worship you! Special rituals will help there. By spending a few credits, you can carry out a ritual that will attract people to your Cathedral. Each follower will provide you with one unit of might. So when the Cathedral gets 1000 followers, you will get +1000 might. The number of rituals is limited to 3 uses per day, but you can avoid that restriction with stimulants!"The number of available Rituals per day increases as the level of the Cathedral increases -- as does the cost of each Ritual.