"Hero" is a class, that has no access to masteries, has three basic traits locked initially and one advanced trait unlocked (like other classes).
Also, he/she has some strong abilities from the start, and possibly free trait and some gear too.
Heroes are unlocked with medals and/or badges.
Examples:
Ash
Starts with chainsaw (cursed) in off-slot and "boomstick" (exotic shotgun) in main slot. If he kills enemy with chainsaw, next shotgun shot take no time. If he kills enemy with shotgun, next chainsaw attack has no time. Free trait:Juggler. Locked traits: Finesse, Hellrunner, Eagle Eye. Unlock : Berserker Silver Badge
Preston
Starts with GCB and Grammaton Cleric Trenchcoat (unique equivalent of A-modded tactical armor). Reload or firing action after moving take no time. Locked traits: SoG, Reloader, TaN. Unlock: Grammaton Cleric Cross
Amazon
Starts with bow (exotic 3d6) ready and endless quiver in off-hand. Locked traits: SoB, SoG, Brute. Unlock: Marksman Silver Badge
Following are more sketchy:
Susan/Reaper
Starts with Grim Reaper Scythe - 6d6 melee weapon that leaves no corpses and Hourglass - non-expendable usable, that teleports you to nearest monster on level with least hp, taking minus one seconds (i.e. giving you 5000 more energy) and making you tired.
Jesus
Saves (turns into living people) formers with touch (fist melee attack). Saved people fight on His side. Melee attack on others have usual damage, but if kills, leaves no bodies. All damage He deals to formers (or people) is reflected back to Him. All damage dealt to Him is reflected back to attackers. When He leaves level, he gains 3 hp per Saved human on level. Locked traits: SoB, Badass. Unlock: Pacifist Gold Badge
Lucifer
If he kills somebody with fist attack, target is instead converted to his side, up to three "alive" at the same time.
Ryu/Ninja
Monster's vision range is decreased by 2, knives damage doubled, all weapons except knives banned. Starts with 6 knives.
Grenadier
Can throw grenades at any time (1s time) expending one rocket. If aimed at self, plants it as mine.