Whenever a character is hit by a lethal wound -- from crew combat, ship combat, exploring, traveling accident or any other circumstance -- they make a Death Save to see if they are able to survive. Basically, whenever your Hit Points reach 0 for any reason, you have a chance to die. Depending on your Game Difficulty, your crew, officers or captains may not die permanently. In those cases, Death Save is not rolled and the character always survives a lethal wound, albeit emerging on the far side with very few Hit Points. The exact number of Hit Points the fortunate character returns with is dictated by the Medical Rating of your ship.
Death Save is rolled as a percentage chance to see if you survive.
Traits such as Lucky, Durable, Survivor all have big impacts on your Death Save and make characters far more likely to survive multiple lethal wounds before finally succumb to the call of the death. Similarly, negative traits like Fatalistic will make characters far less likely to survive lethal wounds.