Bullet-time is a special ability that allows the user to perceive time at a slower pace, which makes it easier to perform combat maneuvers that would otherwise be difficult. It is also used as a visual effect. It has been shown that it slows down time to the point that muzzle flash can clearly be seen fading away. It is usually dignified to be used by the screen being given a red tint. The concept originated from the 1999 film, The Matrix.
In Madness Combat 5: Depredation, Hank used it thrice against 1337 agents. In Madness Combat 6.5, bullet-time is used as a visual effect to detail a M203 grenade that Deimos fired at three A.A.H.W. units, right before they were blown up by the grenade. In Madness Combat 7: Consternation, Hank used it again, this time to fire a Saiga-12 directly into Mag Agent: Torture's face. In Madness Combat 8: Inundation, Jesus used it to use a Mag Agent: V2's Desert Eagle against him, and then again to dodge a dozen rounds from the Auditor's minigun.
In Madness: Project Nexus, it is an ability that the player can use that slows down all gameplay, excluding bullets, which is powered by kills. It takes about 20 kills to completely fill the Bullet-Time bar at the top of the screen. Despite what the tutorial says, the Bullet-Time bar does not have to be completely full to be used. In the last two levels of Episode 1.5, the Bullet-Time bar is replaced by a "Magic Bar".
To view an article on the bullet time visual effect from Wikipedia, click here.