Here’s a photo of what a typical HSMM-Pi mesh node looks like (while resting on my garage floor):
If the node were configured as an internal mesh node, then the wired Ethernet port on the Pi would be connected to a switch linking it with computers, or to a single computer via an Ethernet crossover cable. Those computers would then be able to access the mesh and the Internet through a mesh gateway, if one exists.
If the node were configured as a mesh gateway, then the wired Ethernet port would be connected to a switch that links it to a network with Internet access. For instance, I would connect the Pi to a switch port on my home Internet router. The router would issue the Pi a DHCP lease that enables the Pi to route traffic through the router and onto the Internet. The Pi will then bridge the wireless mesh network to the wired network.