A layer 3 VPN is one in which layer 3 IP headers are used to make forwarding decisions. Like all VPNs, a layer 3 VPN is distinct from normal IP forwarding in that forwarding isolates one VPN from another.

In the words of the IETF:

The logical structure of the VPN, such as addressing, topology, connectivity, reachability, and access control, is equivalent to part of or all of a conventional private network using private facilities [RFC2764] [VPN-2547BIS].

In this document, we are concerned only with the case where the shared network infrastructure (VPN backbone) is an IP and/or MPLS network. Further, we are concerned only with the case where the Service Provider’s edge devices, whether at the provider edge (PE) or at the Customer Edge (CE), determine how to route VPN traffic by looking at the IP and/or MPLS headers of the packets they receive from the customer’s edge devices; this is the distinguishing feature of Layer 3 VPNs.”

Source: IETF RFC 4110 A Framework for Layer 3 Provider-Provisioned Virtual Private Networks (PPVPNs)