Most commonly used on slaves as an incentive to be obedient and not try to leave without a say-so. They explode via remote trigger, however will also explode if someone attempts to interfere with the collar's wiring as it will activate a self-destruct function.
The Brotherhood of Steel will force the Courier to equip one when they first meet as a way to make sure the Courier does not reveal their location to the enemy (unless the Courier is accompanied by Veronica Santangelo). The captives in Dead Money (including the Courier) and Mrs. Weathers and her two children, Kenny Weathers, and Sammy Weathers from the quest Left My Heart are also equipped with them.
These collars are said to be pre-War items. Their use is unknown, although Elijah hypothesizes that they may have been made because pre-War corporations had "compliance issues".
There are various kinds of explosive collar, see the overview for a breakdown.
Spawning this item in the console then fast traveling to another location will cause your head to explode instantly after the loading sequence. This will happen even if you are not equipped with the collar.
Giving the collar to a companion will still kill you.
If you cause Elijah to explode your collar in Dead Money, you are awarded credit for the kills of the other collars, making it possible to easily acquire perks such as Lord Death as you die.
If you find yourself in the middle of Still in the Dark, and you want to go back and get Veronica so that you don't have to kill the Ranger, you must first use console commands to reset the quest and then use it to remove the explosive collar.