At its most basic level (after making a “possibility of life” decision – see below) triage is “4 Bs”:
Breathing
Bleeding
Broken
Burns
Someone who is not breathing has to be enabled immediately, or brain damage and then death will occur within just a few minutes.
Profuse bleeding can kill, too, but even heavy bleeding will slow within a few minutes (longer than it would take someone to die of oxygen starvation, even if “not much longer”) because of reduced blood pressure and the body’s natural reaction to clot and collapse arteries and veins as pressure reduces. So you have “a little” more time to treat that person.
Breaks can get worse very quickly, but they aren’t generally life-threatening. Compound breaks include bleeding, but not usually arterial bleeding, and infection under the skin, which is also dangerous. If you’ve got a broken leg – even with a bone sticking out of your skin – lie over there while we get this person breathing and then that person’s heavy blood loss stanched.
Burns, as painful and dangerous as they are, can be treated after those other injuries are handled.
Of course, any one of these injuries can also include shock, which can lead to heart attack / failure, unconsciousness leading to collapse, etc., and those things can lead to or cause worsening of additional injuries or new and potentially fatal injuries.
Triage, in general, is the process of managing your Emergency waiting room so that the most severely injured people – who still can be saved if treated properly and timely – can be saved with the least additional injury, and no death if possible. That also includes evaluating the condition of the person who comes through the door to determine “does he even have a chance at living at all if we devote resources to him now”.
If a drowning victim is wheeled into the ER, cold to the touch, pale and obviously not breathing, and the rescuers tell the triage nurse that he was underwater for a half-hour, he’s not going to move to the head of the line ahead of a person whose breathing has also “just stopped”. The warm body will be treated first if there’s a resource issue (there is nearly always a resource issue) because that person has a better chance of actually being saved.
That’s all “in general”. Like most other human endeavors, sometimes people aren’t sufficiently trained, and sometimes they make bad decisions even when they are.