Vulkan is an API that gives developers that gives direct access to the GPU and it's very, very efficient. It's suppose to be faster than OpenGL and DirectX. Support for Vulkan range from desktop PC graphic cards all the way down to mobile phones, such as the Samsung Galaxy S7. If you want the fastest graphics performance, Vulkan seems to be the new way to go.
Bethesda has gone and added Vulkan support to DOOM yesterday allowing for faster graphics and it could benefit those with older cards as well. Those with either AMD or NVIDIA cards will be able to take advantage of this.
For a game like DOOM, which relies on the game being as fast as possible, this is a pretty good addition. I might have to pick this up now to see how much faster Vulkan is compared to OpenGL or DirectX.