Each LibreRouter works as a wireless access point, enabling people with phones and computers to connect to it over WiFi.
Each LibreRouter also has two wireless radios and antennas that allows them to connect to other nearby LibreRouters.
They do this in order to work together to interconnect everyone that is connected to each of them.
So if you are connected to one of them, and your friend is connected to another of them, and there is a connection in between the two LibreRouters you are connected to or a path of connections of LibreRouters in between you and your friend, you will be able to connect and share information, do calls or whatever you want the network to be used for.
The way they accomplish this is by physically creating wireless links between them, and then by collaboratively moving information through them so they can make it get from were it is to were it was requested.
At the network protocol level, the LibreRouter’s Operating System (LibreRouterOS, based on LibreMesh) uses a combination of batman-adv and babel mesh routing protocols.
A mesh routing protocol is a piece of software on the router that coordinates actions with other routers in order to collectively move information through the network, allowing the devices that are connected to each of them to talk to each other seamlessly.
There is much more into it than this, but this are the basis.
For more information you can check the LibreMesh website.