Ever since the very first episode of Game of Thrones, we've gotten glimpses of some darkly magical creatures. You've all seen those tall scary men with blue eyes and those crazy skeleton-zombie creatures: White Walkers and wights. Both creatures are featured prominently (and terrifyingly) throughout the show. The Game of Thrones world can be remarkably confusing, so let's take a minute to clarify what exactly these figures are. (Note: this is an explanation of the creatures based on what the TV series has shown of them, not based on what the books have said.)
Created by the Children of the Forest and led by the legendary Night King, White Walkers may look vaguely human-like, but they are far from it. Often appearing on horses, they are much taller than humans and have wispy white hair, a mummy-like appearance, and glowing blue eyes. Their presence brings a chill, and they can freeze things with a mere touch. This makes them extremely hard to battle, because they can freeze and shatter swords. Luckily they aren't impossible to defeat: Jon Snow is able to shatter a White Walker with his sword, Longclaw, because it's made of Valyrian steel. Dragonglass (obsidian) and Valyrian steel are basically kryptonite to White Walkers. Still, these supernatural beings, neither dead nor alive, are bad news.
One of the scariest abilities White Walkers have is the power to create creatures known as wights. Wights are reanimated corpses, like zombies, who are under the control of the White Walkers. The physical condition of the wight depends on what their body looks like when they're turned from a corpse into a wight. So if a body has been dead for months and a White Walker turns it, it's going to be bony and decayed. At the end of season five's "Hardhome" episode, the Night's King turns an entire village of Wildlings (including this Pitch Perfect star) into wights, and since they're all newly dead, they retain their mostly human appearance. The big physical difference is that no matter what color eyes the person had while they were living, all wights have glowing blue eyes to match the White Walkers'. The only way to destroy a wight is to burn it, which is why Wildlings burn their dead. These guys are also bad news.
There are a small number of White Walkers, and they possess terrifying powers. Wights are a product of White Walkers, and they're essentially undead pawns that the White Walkers use to fight their battles. We also learn in season seven that if you kill a certain White Walker, you kill the wights it created — which is why Jon seems so hellbent on going after the Night King in the sixth episode.