Masks are a type of unlockable item in Hotline Miami. At the beginning of most of Jacket's chapters in the first game, the player chooses a mask for him to wear. Jacket has 26 unlockable masks in total, each providing a unique effect, except for the default mask.

Jacket's Masks

Richard (Rooster)
Default mask - grants no special abilities

Rasmus (Owl) - An Eye For Secrets
Obtained by achieving a high score in The Metro - highlights unlockable masks and puzzle pieces

Tony (Tiger) - Fists of Fury
Obtained by achieving a high score in No Talk - faster executions and killing blows from fists

Aubrey (Pig) - More Guns
Obtained by achieving a high score in Overdose - spawns more guns

Don Juan (Horse) - Lethal Doors
Obtained by achieving a high score in Decadence - slamming doors into enemies will kill them

Graham (Rabbit) - Walk Fast
Obtained by achieving a high score in Tension - makes Jacket faster

Dennis (Wolf) - Start With Knife
Obtained by achieving a high score in Full House - gives a knife in the beginning of the level

George (Giraffe) - Look Further
Obtained by achieving a high score in Clean Hit - allows to look further when holding down shift

Ted (Dog) - Dogs Don't Attack
Obtained by achieving a high score in Neighbors - dogs sprint after Jacket, but will not attack

Rufus (Elephant) - Survive One Bullet
Obtained by achieving a high score in Push It - Jacket won't die when hit by the first bullet

Rami (Camel) - Extra Ammo
Obtained by achieving a high score in Crackdown - adds 1/3 more bullets to the magazine

Willem (Monkey) - Rip And Steal
Obtained by achieving a high score in Hot & Heavy - steals enemies' weapons while performing a standing execution

Peter (Unicorn) - Quiet Gunshots
Obtained by achieving a high score in Deadline - reduces the noise of gunshots

Zack (Frog) - Longer Combo Window
Obtained by achieving a high score in Assault - makes the combo multiplier last longer

Oscar (Mole) - Darkness
Obtained by achieving a high score in Vengeance - the game gets a red filter

Rick (Fox) - Good Shot
Obtained by achieving a high score in Safehouse - gives better accuracy and less spread with shotguns

Brandon (Panther) - Walk Faster
Obtained by achieving a high score in Fun & Games - makes Jacket even faster

Charlie (Octopus) - More Melee Weapons
Obtained by finding in Safehouse - spawns more melee weapons

Louie (Chameleon) - Hard To Spot
Obtained by finishing the game with the normal ending - makes Jacket harder to be detected

Phil (Fish) - French Translation
Obtained by finding in Resolution - makes a bad translation of all dialogues to French

Nigel (Bat) - Reversed Controls
Obtained by finishing the game with the secret ending - reverses the controls on the keyboard

Earl (Walrus) - Survive Two Bullets
Obtained by finding in Overdose - Jacket won't die when hit by the first two bullets

Jones (Alligator) - More Gore
Obtained by finding in Full House - makes kills and executions bloodier

Carl (Locust) - Start With Drill
Obtained by finding in Push It - gives a drill in the beginning of the level

Jake (Cobra) - Killing Throws
Obtained by finding in Hot & Heavy - kills enemies when throwing weapons at them

Richter (Rat) - Start With Silenced Uzi
Obtained by finding in Assault - gives a silenced uzi in the beginning of the level

I got most of the information from the Hotline Miami wiki

http://hotlinemiami.wikia.com/wiki/Masks