AMD states that "Vulkan supports close-to-metal control, enabling faster performance and better image quality across Windows 7, Windows 8.1, Windows 10, and Linux. No other graphics API offers the same powerful combination of OS compatibility, rendering features, and hardware efficiency."
Vulkan offers the ability for game developers to have more granular control over components, which in theory can allow for a boosted gaming performance. So, developers can manage certain things like memory allocation and the generation of GPU workloads, which lets them gain more power out of multithreaded systems.