If someone's unhinged, they aren't completely sane. Unhinged is another way to say "crazy" or "out to lunch."
Babysitting six kids between the ages of three and ten for an entire day might leave you feeling a little unhinged. More serious is when voters begin to worry that one of the presidential candidates is actually unhinged, appearing irrational and unpredictable. Unhinged stems from the less common verb unhinge, which meant "disorder the mind" before it was ever used to mean "take a door off its hinges."