The term Red Shirt
refers to security personnel from the USS Enterprise in the original Star Trek
series, sent along on Away Teams, presumably to protect the more familiar characters. Unfortunately, they usually just ended up being killed, often times off-camera, by whatever was menacing the ship and crew in that particular episode. Thus, to suffer a Red Shirt Death is to be killed quickly, pointlessly and ignonimously.
When Tasha Yar got killed by that stupid tar monster, that was a total Red Shirt Death.