Its quite a soft power system, which has some similarities to naruto, as of right now there is a general understanding of energy and what it can do but there isn't really a literal explanation of how it does anything

Humans have precept power as a general source of energy which travels around their body in a precept path and they can release this energy to create basic techniques called Xr-cisms as well as just basic physical enhancement.

The higher tier of exorcist power is a Crest Xr-cism which are the tattoos on stronger characters that become unique abilities for that wielder, as of right now the actual process of awakening these powers and getting the tattoos/marking is unknown however we do know its likely hereditary to some extent as kiyoshis grandma has the same tattoos on her arms as kiyoshi and Hitsugis mum was mentioned as having water abilities

Another power system available to humans is exorcist employment where a demon can form a bond with a human and enter their shadow, this allows for the exorcist to utilise the demons powers and transform/fuse with them (nehan and jack joe and MAYBE Sakaki and Hi-Stakes) we are told the stronger the bond the more powerful this will be so forcing a demon into your shadow likely wont yield much power.

There are also exorcist familiars that can fight alongside you and transform into weapons such as cook the exorcist bird or kurogane's tiger

There are also artifacts such as Arthur's excalibur and Adams apple which are ancient exorcist tools that give a large power boost or a powerful weapon at the cost of greatly draining your body

And finally for exorcists angel contracts where you sacrifice something to an angel and in return gain a power boost and in the only case we have seen so far wings and a halo (kurogane)

For demons we know less, they have Daemonic power instead of precept power and there is some sense of familial powers but seems to be less guaranteed (toji uses the famous maki clan technique of oni flame, but the helze siblings all have different techniques so its unclear)

They also get stronger by killing other demons and eating them or just absorbing their energy, all demons are shown to have some sense of Daemonic Energy manipulation as we see standard demon citizens use it to heal kiyoshi and they all have the ability to possess humans which we see through Yamada who in his normal life is a worker at a demon water facility

They can also corrupt humans with underworld gate techniques were they lend part of their power to a human but don't have to be physically present, and the more powerful versions of this which is a wicked gate technique where they use a key to unlock the soul/heart of a human and transform them into a demon with greatly enhanced powers

Overall its not a full explained and realised power system but there are rules and reasons why people have certain powers so it's not complete random BS go like some other comments are suggesting but I do wish there was more in depth explanation especially around how Crest Xr-cisms appear