One sentence:
Satanism, to me, is the promotion and seeking of liberation, individual empowerment (which leads to collective empowerment) and the cultivation of compassion.
Longer:
I see Satanism as being "anti-natural" in that it supports the disruption of the natural order. As Satan disrupted the natural order of human evolution by bestowing His Black Flame upon our species, we also disrupt the natural order by making changes that serve our needs instead being at the mercy of life's whims. Medicine is an example of this. We work to eradicate diseases and to elevate the general welfare of all. We went from being sickly creatures where most of our children die in childbirth to being much healthier in general and living much longer lives on average. This is thanks to human ingenuity.
With this power, we can use it to alleviate the suffering of not only human beings, but other lifeforms as well. We can combat the tyranny of the natural order that is placed on us. Satanism is to stand against tyranny and the biggest tyranny is that of nature. Lord Satan gave us the gift to become divinities and He has suffered character assassination and scorn. This is His being thrown from Heaven, that is His having His liver eaten while chained to the rock. But He endures the hatred of the misinformed and the uninformed and continues to inspire us in loving forbearance. So we must embody the compassionate example set by Satan when He took notice of a lowly group of apes and removed their blinders.