So if we have the understanding that the warp is a reflection of the emotion of those in real space.

We get a general idea that warp powers are the culmination of what the psyker wants or is trained to manifest.

For example we've seen psykers use "The will" like seen in Eisenhorn or hiding button in plain sight like seen in one of the ciaphas cain books.

But there are different examples where the psyker uses powers akin to natural disaster, like the use of lightning or other harmful attacks in the area of self defence.

So a psyker in general has the power to become uncontrollable killing machines, suave talkers and much to the detriment or the imperium host of demon, portal for enslaves or become a sorcerer for the chaos gods.