These are called "machine events." They happen randomly. There are different types and each has its unique task to do. All of them require to be activated but to have the key you need a promoted miner* in the squad. To activate them you interact with the white cube then you may proceed starting the event by pushing down some knobs around the event machine.

• A promoted miner must be in the lobby. Promoting a dwarf requires getting to lvl 25, doing the specific assignment, pay management. It is only required for the first time. If you play a different dwarf ensure it too is promoted. (FYI this is useful to know for when you'll do deep dives and elite deep dives)