As the name suggests, this technique is simply a soundless method of killing an opponent, usually from behind with a blade. Additionally, because the user moves silently, the attack cannot be anticipated and defended against. The user will often slit their opponent's throat, preventing any cry that might give them away. Some shinobi also opt to use a cover such as mist or even frost to rob their opponents of their field of vision and then attack them.
Although the name of this technique is written in kanji (無音殺人術), it's pronounced in English ("silent killing" (サイレント キリング)). The Japanese pronunciation of the kanji would be Muon Satsujin Jutsu, which would literally translate to "soundless murder technique".
According to Kakashi, this technique allows the user to kill their opponent so quickly, that they die before realising it.
In the anime, Mizuki attained the Silent Killing technique when he spent a year in the Konoha Strict Correctional Facility, where his eyes became attuned to the dark and damp environment. He was able to move seamlessly through the darkness, repeatedly attacking Iruka undetected.
Silent Killing may have been inspired by various Chinese and Japanese books released during the centuries detailing various ways to be stealthy, and how to silently kill another person using various weapons and by targeting vital organs in the body.