“With this Perk, you now have the ability to move quickly and still remain quiet. You can Sneak, and run at the same time. Without this Perk, you would automatically stop Sneaking if you ran.”— in-game description, Fallout
Silent Running completely negates all movement penalties, regardless of movement speed. The detection level for the player character is the same when standing still or moving around, no matter if moving slowly or running. Without this perk, the movement penalty for moving slowly is 10% and 20% for running. Detection is measured based on a scale of -100 to 0. At -100, the player character is undetectable. At -20%, enemies will enter [CAUTION] mode and start searching. When the detection level reaches a positive number, one will be detected. Without Silent Running, an enemy who doesn't detect the player character (at detection level -30) will immediately enter [CAUTION] mode if one runs towards him, as the penalty will increase the detection level from -30 to -10 right inside the critical stage. With the Silent Running perk, one can move closer and the enemy will not detect them as long as the detection level stays below -21. The player character's speed doesn't matter, since there is no penalty for movement with this perk. Whether moving slowly or running, it will equate to standing still. The numbers above apply to enemy Perception based on sight. Sound-based perception is affected as well with high sneak, regardless of footstep sound generated.
With this perk, 100 Sneak and a cloaking field (with Stealth Boy and/or Chinese stealth armor in Fallout 3), the only way to be detected is by shooting enemies with a loud weapon repeatedly, or by walking into them.
Despite being labeled as "silent" running, one still generates the same amount of noise from their footsteps as usual, but non-player characters don't react to it.
"Silent running" is a mode of operation for submarines where all unnecessary systems are shut down, propeller speed is reduced and the crew is ordered to remain as quiet as possible, all in order to reduce the chances of being detected by passive sonar.
The following is based on unverified behind the scenes information and has not been confirmed by canon sources.
It may also be a reference to the 1972 film Silent Running, which was set against a post-apocalyptic sci-fi backdrop following the extinction of earth's plant life and features several prominent nuclear detonations throughout the film.
End of information based on unverified behind the scenes information.