Satanism is this big word for many religions that worship Satan. Though Satanism flourished in the 1960s, it actually has roots way back in history. Take Milton's Paradise Lost for example. This 17th century work had Satan as one of the central characters, and has him explaining why he doesn't want to serve God. Satan in this work questions God as his creator, throwing the known universe into disarray.
Fastforward to the present, and we see many people becoming believers in Satanism. Why? The internet allows us to get information quickly, and a google search on Satanism can get you to various churches that practise it. There are Theistic Satanists - i.e. those who really believe that Satans exist and worship him, and Atheistic Satanists - those who use Satan as a metaphor to convey their belief in choice, and that they should take responsibility for whatever happens in their own lives, not God.
Sidenote: Theist means God, and Atheist means without God, so you can derive what these words mean easily from these opposing terms.
La Veyan Satanism is part of Atheistic Satanism, and Our Lady of Endor Coven is part of Theistic Satanism.
I don't know much about Satanism to elaborate fully on its ideas and beliefs, but I do think this came about because people found Christianity to be problematic. Satanism is a reaction against Christianity - Atheistic Satanists find it illogical that they should trust a higher power to organize their lives. They rebel against God and instead seek to make responsible choices. Satanism also stems from people who are disgruntled by what they think are illogical loopholes of Biblical teachings, and they think this other belief will provide them with the answers they are looking for.
I also do think that Satanism is part of the backlash that comes with evangelizing - no one likes being told that they are going to hell for not believing in the one true God, or that their religious beliefs are wrong. Satanism is a more extreme form of rebelling against these sentiments.
Naturally Christians are very upset with this. People are worshipping the devil himself, who supposedly tempts people to make immoral decisions. Perhaps they also think that these teachings are not aligned with their own and are crude ideas cobbled together.
As with all religions, tread carefully. Read up on them to know what they are and how they function, and never insult someone else's religion; respect the person and his choices, even though you may disagree.
