The Plague Doctor mask dates back to the 1500s and is a very traditional Venetian masquerade mask.
It was used by doctors to filter the germ laden air during periods of plague, which were very common in past times. It was a pre-cursor to the gas mask.
The doctor usually held a stick in his hand, so as not to come into direct contact with the afflicted and wore impermeable clothing, made from waxed canvas, which also sealed the edges of the mask around the face. The mask itself had glass over the eye holes. Air could only pass through two slits cut in the 'beak' and was filtered by aromatic herbs pressed inside.
For these doctors however, the disease was not caused by air borne microbes (which were not discovered at this time), but by spirits. They wanted to keep the spirits at bay by frightening them, which explains the terrifying appearance of the costume.