The promise of most mesh nets is that they're (more or less) a self-configuring distributed VPN. Give a node some credentials and (usually) a few real, publicly-routable IP addresses to "bootstrap" nodes, and that's it. It's on the network.
There's no "real" network that they provide a gateway to, necessarily, just a bunch of nodes, potentially none of which are on the same physical or logical local network, aside from the mesh network itself, which is an overlay network—think of an overlay network like a virtual machine, but for networks, incidentally: a protocol stack built on top of, or within, if you prefer, another protocol stack. You feel like you're talking TCP/IP over it, but under the hood your TCP packets are carried in other packets (may or may not also be TCP—often it's UDP when possible) over the normal Internet, then reconstructed back into this virtualized, if you will, packet stream on the other end.
With a traditional VPN, you'd connect to a real device that provides a gateway to, say, a corporate network, which may have routing connecting multiple locations but is essentially a normal network. Mesh networks operate much more peer-to-peer than that, usually leveraging known peers to find routes to others that are (for whatever reason) unreachable or initially unknown. The "mesh" part refers to the routing, mainly, the job of which is to search out and find good paths to nodes. If "corporate" has fiber cut by a backhoe, "the VPN" isn't down—many, many nodes might be, but the network might survive in a useful form.
