LXC is like a chroot jail on steroids. For sake of argument, you can consider it a light weight VM (even though it's not a VM at all).
If you've already gone through the effort of writing an application that is designed to live on ephemeral infrastructure, then LXC just lets you do it with less overhead.
For me, the coolest thing about LXC is the community growing around it. Consider something like docker - a docker image is relatively portable. It provides the tools to configure identical containers on physical hardware, or within a VirtualBox VM running on your desktop, or within VM's provided by Amazon or Rackspace. This brings us closer to the dream of write-once run-anywhere.