Vulkan (API) is OpenGL2 graphic cards

Vulkan (API) is next generation OpenGL in short you can call it OpenGL2.
The benefits with Vulkan and DirectX12 it will be faster and works closer to hardware.

To make the older graphic cards support Vulkan it is done by driver updates but some older graphic cards  will not be supported by Vulkan (API)
Nvidia and Khronos Group said  "we are not planning to support Geforce 400-500 class GPUs"

For AMD graphic cards to support AMD:s Vulkan (API) it need to be architecture Graphics Core Next (GCN), it means from Radeon HD 7000 and newer that will have support for Vulkan (API)

So in short Nvidia graphic cards from Kepler Geforce GTX 600-series and newer will support Vulkan (API) and if you have older graphic cards then it will not support it.

More info about Vulkan (API) by Khronos Group 1hr 21min video: Link