After the Galactic Empire was destroyed at the end of star Wars VI - Return of the Jedi, the Empire split into different factions. The faction that Star Wars - The Force Awakens runs with is called The First Order is lead by Supreme Leader Snoke.
The First Order has built a new Death Star but this time its an actual planet turned into a weapon that can destroy whole solar systems, its known as the Starkiller Base. You don't see Snoke apart from a scene where he is communicating with General Hux and Kylo Ren using holographic technology, similar to what Palpatine used to talk to Darth Vader in Star Wars V - The Empire Strikes Back.
The description of the First Order in the text that scrolls up at the beginning of the film is that they wish to find and kill Luke Skywalker.