What a hypervisor does
A hypervisor slices one physical machine into isolated virtual machines, each with a full guest OS. Type 1 runs directly on hardware (ESXi, Hyper-V, KVM) and is what clouds use; Type 2 runs as an application on a desktop OS.
Hardware support
Intel VT-x and AMD-V let guest instructions execute natively rather than being emulated, and IOMMU/SR-IOV pass devices through with near-native I/O. This is why virtualization overhead is now small enough to be irrelevant for most workloads.
VMs versus containers
A VM virtualises hardware and boots a kernel — strong isolation, gigabytes, tens of seconds. A container virtualises the OS, sharing the host kernel — weaker isolation, megabytes, milliseconds. MicroVMs such as Firecracker sit in between and back many serverless platforms.