Does anyone know what this container is?

The heater matrix (heater core) for the cabin heater is in that box.

It is likely that the matrix (core) is corroded and will need replacing. It looks like it should be fairly easy to access it, unlike on some vehicles where you have to totally remove the dashboard.

First thing to check is that the leak isn’t just from one of the two pipes that can be seen connecting to the matrix (core). If it is leaking from the pipes, you may be able to disconnect them, clean any corrosion and refit them.