The Armstrong Limit (named after USA Air Force general Harry George Armstrong who discussed this), is the pressure where water boils at the normal temperature of the human body. At pressures less than this, an oxygen mask is insufficient, a pressure suit is required. The Armstrong limit is about 1/16 normal air pressure (0.063 bar).
If Mars could be terraformed so that the air pressure is above this (say at 0.1 bar) humans could go out onto the surface with regular clothes and a tightly fitting breath mask.
Effects of an Unprotected Person on Mars
First the air would be sucked out of the lungs. It is advised to shout as this happens to avoid damaging the alveoli in the lungs. With no oxygen in the blood, the brain will become oxygen starved and the person will fall unconscious, within 15 seconds. You would likely die within 100 seconds of depressurization.
Exposed fluids will start to boil, including tears, saliva, and fluids wetting the alveoli inside the lungs. The blood inside the body will not boil.