Tourniquets are tight bands used to control bleeding by completely stopping the blood flow to a wound. Tourniquets work only on arm and leg injuries; you can't exactly wrap a tight band around a patient's neck and cinch it down to stop the flow of blood.
Traditionally, tourniquets were reserved for the worst bleeding to keep the patient from developing shock.
The use of tourniquets was first documented on the battlefield in 1674. Complications of tourniquet use were said to lead to severe tissue damage. Soldiers had amputations of limbs that were often attributed to the use of tourniquets but could have just as easily been from infection. Eventually, tourniquets developed a bad rap in the field of emergency first aid.
Applying a tourniquet in the civilian world used to be seen as a last resort. It was thought that they made sense for soldiers because combat wounds are severe and a fighter needs to fight. A tourniquet can be applied and ignored.
That doesn't mean tourniquets don't work. On the contrary, tourniquets can arrest bleeding quite well and are certainly useful in cases of severe bleeding that cannot be stopped any other way. They're popular on the battlefield because they can be applied quickly and do not need to be constantly monitored once they are in place, allowing even injured soldiers to remain conscious and continue fighting.