To close, terminate, or end.
They are planning to shut down the entire building at the end of the month.
To turn off or stop.
It's a good idea to shut down the machine before you leave.
To emotionally withdraw into oneself as a defense mechanism; to block out external stressors.
I can't talk to him about a certain thing; he just shuts down anytime I try.
(auto racing, car culture) To pass (another vehicle), especially quickly.