The full system, means, all your standard stuff works in expected way - crons, systemd units, sshd, multiple users, your regular backup solutions and so on. As well, that "system" can be dumped/exported/backuped/snapshotted as a whole - very much similar like you do with your vSphere/Qemu or whatever you use in your datacenters as hypervisor.
Foreseeing the question - yep, you can run Docker inside LXD/Incus VEs. In practical terms, that makes much simple when you need to give some dev team (who are of course not anywhere known to do sane things) access to environment with Docker access (which in 99% cases means that host's root level access is exposed).
LXC containers used in incus run their own init, they act more like a VM.
However incus can also execute actual VMs via libvirt and since recently even OCI containers like docker.