LXC is OS-level virtualization (similar to openvz and plain old chroot), which has a much lower overhead compared to full virtualization (i.e. virtualbox, kvm, xen hvm) but requires that the guest share the host's kernel. You get easier setup (untar the filesystem and tweak a few config settings) with stuff like LXC, but you obviously cannot run Windows/*BSD/whatever.

> What does this technology let me do that I can't do with stuff like virtualbox?

Fit more containers on your host :)

Share (disk and memory) resources among your containers

Make the same partition/directory/files available to a few containers at the same time without using ssh/nfs/smb/etc

... and so on.