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.

VMs each have their own kernel, but containers share the host kernel. This tends to be more efficient and doesn't require you to statically allocate vCPUs and vRAM upfront when you create a container.

LXC also has an under-appreciated mode where you can run some processes (but not a full OS) in a container.