It requires the subduing of prey, usually completely on the ground and pinned by the predator, and the engulfing of the muzzle of the prey entirely in the mouth of the predator, blocking respiration through either the mouth or nose.
[1] It is generally easier for large, social carnivores to use this method with large prey when there are multiple individuals holding the prey still while it suffocates, in the case of the lion, or for solitary carnivores killing weak or small animals.
It is also a calculated measure not seen often because most predators are known, especially canids and hyaenids, for eating the prey while it's still alive and letting it die of loss of blood and/or shock, not bothering with killing it first.
This method also silences the prey for the most part and can be used by solitary animals to keep the noise down as not to attract other predators with the commotion.
If the predator is too tired, it may resort to another method of killing or withhold from finishing the prey off until it catches its breath.