Anything which joins a layer 2 network to another through a shared medium could be considered a layer 2 VPN.
Consider an office building where I rent rooms 1 and 101 and you rent 2 and 102. The building management gives me ethernet sockets on a single broadcast domain in both my rooms. Your sockets connect yours.
If it's done with a piece of Cat 5 at a patch panel we'd just call that a private ethernet. If we partition a shared thing, it's virtual. If the rooms are close it might be done with VLANs and trunks which would be entirely invisible to you and me. If far perhaps with MPLS or whatever.
Per your question: we're joining smaller pieces of a private network into a larger one, through a shared medium we want (at least) addressing privacy from. Per netztier's comment, you can also take the building management's point of view: we're partitioning off private portions of a shared, larger, thing.
(In layer 3 VPNs it's usual for the closing off to be done by the "client", but your can certainly buy virtual point-to-point links from lot of ISPs.)
In essence the "virtual private" part describes that there is a medium which is shared in a way which is invisible to us, at least from inside the border equipment.