What could have caused me to have passed out at the orthodontists office all of the sudden?

Several things: Vasovagal syncope is a response where people panic and it causes the flight or fight response. Unfortunately your brain is not ready for it and only part of the response gets activated- which causes a drop in blood pressure causing you to faint. Another cause could be low blood sugar.

Several reasons: Orthostatic hypotension (drop in blood pressure with a sudden change in position resulting in decreased blood flow to the brain) could be one cause. Other possible causes, an irregular heart beat, a drop in your blood sugar, anxiety, or receiving your bill.