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.
Except if you're really pressing and you find your character walking too slow in Sneak, this perk is not very useful (especially the risk situations in sneak are very rare).
With this perk, you gain +10 Sneak and running no longer factors into a successful sneak attempt.
This perk drastically increases your ability to crouch-run through buildings getting free Sneak Attack Criticals on everything in sight. Together with the Chinese stealth armor, the player is virtually invisible to non-player characters even when using the Pip-Boy 3000's light. For combat, consider using a silent weapon such as a melee weapon, or a gun with a silencer such as the Perforator or silenced 10mm pistol to remain undetected.
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 around. 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, you are undetectable. At -20%, enemies will enter Caution mode and start searching for you. When the detection level reaches a positive number, you get detected. Without Silent Running, an enemy who doesn't detect you (detection level -30) will immediately go into Caution mode if you run towards him, as the penalty will increase the detection level from -30 to -10 right inside the critical stage. With the Silent Running perk, you can move closer and the enemy will not detect you as long as the detection level stays below -21. The player's speed doesn't matter, since there is no penalty for movement at all with this perk. Whether you move slowly or run, the game will always consider you to be 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. Uncomfirmed for lower sneak levels.
With this perk, 100 Sneak and a cloaking field (with Stealth Boy and/or Chinese stealth armor in Fallout 3), the only way for a character to detect you is by shooting him with a loud weapon repeatedly, or by walking into him.
Despite being labeled as "silent" running, you still generate the same amount of noise from your footsteps as usual, but non-player characters don't react to it.
"Silent running" is a mode of operation for submarines: all unnecessary systems are shut down, propeller speed is reduced and even the crew is ordered to remain as quiet as possible, all in order to reduce the chances of being detected by passive sonar.
With this perk, your running no longer factors into a successful sneak attempt.
If you are a melee or unarmed fighter and rely on sneak attack criticals then this perk goes very well with Travel Light, Implant M-5 and Tunnel Runner allowing you to close the distance quickly while remaining silent so you can achieve a Sneak attack critical.
Edit