It seems a bit connected to online trends. The ISP suggested using it as an extension for your LAN, but you're having trouble opening it. You might want to look up tutorials on how to access it properly.
I believe there could be a barell connection, so I’m extending the Ethernet cable for female-to-female use. It doesn’t seem like an active repeater.
It seems the bromine has mostly replaced the plastic components in this setup. This probably means a straightforward female-to-female adapter to connect two cables together. You can use it (though I’m hoping the internal wiring supports gigabit speeds) or opt for a longer cable. It doesn’t appear to be a powerline adapter, so a standard wall plug should work.
We have these in the job, I believe. Several Ethernet connections are present. They connect to Ethernet ports. Keep in mind, I'm working in a dusty warehouse.
Are there any ports on the side you didn't show us? Or just those small cutouts on the one side? If there's no power outlet, then it's not a repeater (A repeater takes the signal for Ethernet, and extends it beyond the 100m limit). It could be a coupler inside. We'd have to see it without the cover to say more.
From what I see, it seems like an outdoor weather enclosure. Its interior isn’t visible since you didn’t manage to open it. Because it appears to be attached to a wall, hold both wings using the screw holes and pull the opposite side of the case. It looks set up with the wings down and the opening facing inward. Lifting the case should reveal its contents—possibly empty, but I won’t know until you take it apart. It might have a good friction seal.