The choking game is not technically a game but a schoolyard activity involving the production of unconsciousness or near unconsciousness by restriction of the supply of oxygenated blood to the brain.
Blood flow to the brain is restricted by compressing the carotid artery in the neck. This is achieved either by pressing the thumbs against the arteries on both sides of the neck simultaneously or the use of a ligature. Apart from the direct restriction of blood to the brain there are two other significant physiological responses to pressing on the neck.
Pressing on the carotid arteries also presses on baroreceptors known as the carotid sinus bodies. These bodies then cause vasodilation (dilation (widening) of the blood vessels) in the brain leading to insufficient blood to perfuse the brain with oxygen and maintain consciousness.
Seriously WTF!! Why would anyone want to do that?!
There are other variations in which involve self induced hypocapnia:
This involves no compression of the neck but requires hyperventilation for a minute, or until symptoms of hypocapnia such as tingling, light-headedness or dizziness are felt, followed by a breath-hold. The effect is greatly enhanced if lung air pressure is increased by holding the breath "hard", that is forcing exhalation while allowing no air to escape. This alone is enough to cause a blackout but usually tradition requires one of a number of other actions such as a bear hug given from behind or pressure applied by another person under or over the heart, usually with the head of another participant.
Again WHY!!!!