Fast monsters is a setting which makes monsters more aggressive.
The more common demonic monsters from the original Doom are the most affected by this mode. Demons and the related spectres move and attack twice as fast as usual. Some projectiles are sped up to 20 map units per tic, making imp and cacodemon fireballs twice as fast than usual, while Hell knight and baron of Hell projectiles are 33% faster. These and other monsters also attack considerably more often, usually moving very little as long as they have their target in sight, which makes hitscan enemies considerably more dangerous, and the player's fist and chainsaw much less useful.
The fast monsters setting is automatically activated when playing using Nightmare! difficulty. In addition, Nightmare! difficulty also adds a special check in the monster behavior code causing all monsters to attack immediately on sight (on all other difficulties, monsters may or may not attack on sight, with the random chance weighted based on the distance to their target).
The setting can be used with any skill level using the -fast command line argument.