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KVM is full machine emulation (i.e. hardware is emulated, and you can run different kernels inside the guests than you do on the host).

Docker uses LXC which is like BSD Jails, most of the advantages of VMs but you don't have to emulate a whole system, there's only one kernel atop which multiple containers/jails can run different software and have thorough isolation. Very fast and light-weight, but you can't run different OS kernels.

nitpicking: KVM stands for "Kernel Virtual Machine". It's an implementation of virtual machines, just like VirtualBox or VMWare. Containers are completely separate from KVM.

That's a great way to describe it. It's a "lightweight" VM that is created per process.