1. His Facial Features are Deformed and Scarred
The look of Supreme Leader Snoke was a closely guarded secret. Even Andy Serkis, the man who did the motion capture for the character, had no idea what he looked like. (At least, that's what he said in interviews.) We don’t know what happened to Snoke, but the man has obviously been through a lot. His face looks to have been severely damaged and he’s got some pretty substantial scarring. What exactly caused this damage is unknown. Are the events that caused his injuries the reason that he is on his current path? Does he hold a grudge against the last living Jedi?
2. He’s Bigger Than We Thought (Or Maybe Not)
One of the things that we learned early on about Snoke was that he was a physically imposing person. He was supposed to be huge. That still didn’t prepare us for the gigantic man we saw on a gigantic throne when we first laid eyes on the Supreme Leader. He towers over General Hux and Kylo Ren in the scenes where they converse. However, then we discovered that he was being projected at that size, and wasn’t actually there. He could actually just be a normal-sized person on the other side. We don't know that answer yet.
3. He's Pulling the Strings on Hux and RenThe First Order has a much greater plan at play here, and Snoke is the one in charge of it all. General Hux and Kylo Ren both report directly to the Supreme Leader. General Leia even blames Snoke for being the one who turned her son, Ben Solo (Adam Driver), to the Dark Side in the first place. Hux and Ren will be problems to be overcome, but Snoke is the real enemy. He calls Ren to complete his training at the end of Force Awakens. Bring on Star Wars: Episode VIII.