Is a neologism for an old-school adventurer in classic role playing games (both tabletop and vidya.) Basically, the characters that go into dungeons to slay the monsters, kill the big foozle, and nick all the treasure. They don't have a home and they gallivant around the world slaying things and stealing their stuff.
Done well, a hack and slash campaign or game in which one is a murderhobo can be rather amusing. After all, why become an adventurer other than to slay things and steal their stuff? A wizard doing unspeakable experiments to goblins in his tower? He's probably got some cool shit - let's slay him and loot the place! A dragon threatens the land and demands a monthly tribute of virgin sacrifices, and Cliff Richard's just left town and Angharad, the lass with the friendly legs who they call the Welcome in the Valleys, is all that's left of the eligible womanhood in the region? Let's slay it and loot his lair! There's an ancient tomb that's been undisturbed for centuries and nobody's at all bothered by it and there's a few undead hanging about out there but generally keeping themselves to themselves? Fuck it, let's eviscerate the undead and steal everything that's not nailed down, and crowbar up the nails off everything else!
While not slaying things and nicking their stuff, murderhobos generally camp out in the wilderness or stay in temporary accommodation, even though by flogging all the loot usually provides them the means to buy outright a home of their own, hence the "hobo" part.
To be fair, earlier editions of Dungeons & Dragons and other role playing games indirectly encouraged murderhobo tendencies. For example, you could gain XP by looting treasure, so stealing everything not nailed down became a valid and necessary way to grind your character up to higher levels. That, and many classic adventures were basically invading an eccentric loner's home purely on the basis that they were a wizard, a demon, or a demilich, and cleaning it out. There was usually some excuse plot point about how said loner might just be plotting to take over the world but little evidence of same in reality.
Of course, this is not to say that a murderhobo campaign can't be fun. A university friend of mine recently mentioned that his D&D troupe was in severe danger of becoming like "a blood soaked Waiting for Godot" but it was the most fun campaign they'd played in a long time. And in the realm of vidya, the best titles generally deconstruct or acknowledge murderhobo tendencies. In The Witcher series, it's mentioned that the titular itinerant monster slayers for cash are hated and treated with disdain because they are, not to put too fine a point on it, professional murderhobos. In Baldur's Gate II the recruitment quest for the dwarven berserker Korgan involves robbing an undead-riddled tomb and if you, the player, express concern at this he says that these undead might just get out and hurt someone so it's really a public service.
I also suppose that murderhobo adventuring was inspired by a lot of early thud and blunder literature as well, in which the hero is usually a well built barbarian type unfettered by civilisation who wanders from place to place seeking adventure, gold, and buxom wenches and who solves problems by beating them to death with a big sword.