"Maxim 1: Pillage, then burn."
- – The Seventy Maxims of Maximally Effective Mercenaries
Adventurer is a title given to individuals whose occupation is, obviously, adventuring. "Adventuring" implies going on adventures, but in practice is more likely to involve murder, security detail, object and artifact retrieval, tomb desecration, and waking things best left sleeping. Adventurers usually have short lifespans, but make up for it by wielding phenomenal cosmic power and carrying around enough material wealth to destabilize the economies of entire regions. Usually Adventurers are also Player Characters. The inverse is even more common.
Broadly speaking, an adventurer's job description will fit into two categories, with some overlap. Both involve killing things, but one is slightly more social than the other.
Murderhobos is a term used (originally pejoratively, but occasionally affectionately) for the player characters in RPGs, both in video games and tabletop games. The term arises due to the fact that most adventuring characters and parties are technically homeless vagrants, generally living on the road and sometimes in temporary accommodation, and the default solution to problems faced by the typical adventurer boils down to killing things until the problem is solved or treasure is acquired. In many games (especially older pure hack and slash-types of the type that Gary Gygax despised) killing things and taking their stuff is simply the order of the day, all morally acceptable and proper, either because that's all the players are interested in doing or all the GM can come up with. In more nuanced settings, "Murderhobo(s)" is used especially to refer to characters (or entire parties) of looser morals who tend to regard massive collateral damage as an inevitable and unremarkable consequence of their actions, or who are quite happy to slaughter otherwise friendly NPCs at slight provocation or the prospect of financial gain (thus often overlapping with munchkins).
Although it is a fantasy standard that adventuring parties are welcomed into towns and villages and hailed as saviors (or at least obscenely rich individuals that are loose with money), there is a small trend for this to be inverted in some games and stories (usually for comedy's sake) and have the protagonists be treated as the homeless serial killers they actually are, either by having them rejected from civilized society or by having the NPCs/minor characters respond with pants-shitting fear whenever the heroes present themselves. Murderhobos left to their own devices are bad news for the region they occupy, so they are often dealt with by giving them quests that take them to dangerous places in distant locations, where they can kill some other monsters (or at least some foreigners).
See, in the dim and dismal early days of RPGs, especially Dungeons & Dragons, gameplay was often seen as a conflict between the DM and the players. It did not go unnoticed by the playerbase that, as with paladins and their strict codes of conduct, many a DM, killer or otherwise, would often immediately seize upon backstory-based connections and abuse them for, at best, cheap plothooks and at worst bad drama - got a cute little sister who wants to be a wizard? Boom, now you gotta rescue her from the ogres before they rape her! Have a wife and kids you're adventuring to generate money for? Boom, they get massacred by an orc assassin! The worst of such DMs would even go after NPCs you took a particular shine to in the course of the game as either plot-hooks or free shots at you: that pie shop you love to visit each time you go to town turns out to be run by a mad cultist who poisons your favorite snack, that cute shepherdess you take a moonlit walk with turns into a werewolf and kills you, that Chaotic Good naga waifu you bring home to your foundling town suddenly goes nuts and eats all the kids at the school she was teaching at and
serves you right for having a Good naga waifu for a wife! Jeez! you gotta take responsibility, etc. Naturally, players weren't exactly thrilled by this.
Hence, the development of the murderhobo; a blank slate character practically hatched from an adventurer egg, with no backstory NPCs to threaten, and who doesn't give a damn about anyone the DM puts down except as they fuel the progression of loot and EXP. The princess you were supposed to rescue from a tower can't suddenly yet inevitably betray you if you've already cracked her skull like an egg and grabbed everything valuable on, in, and around her.
Murderhoboism is invariably a metagame effect. It's a conscious decision by the player not to have attachments that a sadistic DM could harm to force a dramatic action. To head it off, the DM needs to make it clear to the players that such things won't happen. It's up to you, Mr. DM, to design the story so the players have ample opportunity to stop harm from befalling their loved ones, and in turn you can get NPCs that act as questgivers and sources of aid and support. Fighting murderhoboism is win-win for everyone.
Mercenaries are people who fight in conflicts for the sake of direct profit provided by their employer. In most fiction, they exist to provide a group of people who have military force capacity, while not being associated with particular political and societal factions. This means that most mercenaries are used for protagonists and anti-heroes, as it's much easier to create a believable and unique character without restricting them to a set group of beliefs of a faction. Equally frequently, the mercenaries are shown in the dark light as well, being pragmatic villains who have little of interest in anything besides money, thus allowing them to be the bad guys by doing anything and everything evil for the sake of wealth.
In many a game, the PCs are hired as mercenaries to provide services for someone, starting from removal of Giant Space Hamsters from the cellar of a local noble, to poisoning the king during a banquet so his brother's cousin's sister can usurp the throne. And, since parties can range from Chaotic Stupid to Stupid Evil to Stupid Good (even at the same time), all characters can act towards a common goal without having to resort to fratricide because they can't agree on an approach to the situation (as most players use their status as mercenaries as an excuse to do things out of character, because "Derp, Money").
Adventuring as a Job
Recently we've seen an influx of new settings where being an Adventurer is an actual, real job description. Often employed in an Adventurer's Guild, this trope plays everything about the typical PC completely straight, but builds it into the setting as an accepted and regular part of life. Need to fix a house? Get a carpenter! Need a troll dead before he steals all your sheep? Get an adventurer!
Increasingly common in medieval animu, it does see some use in western settings as well. Order of the Stick has run with this since the very beginning, but since its a self-aware pastiche of RPGs in general, that's to be expected. Many a DM create similar worlds, since that completely circumvents the need to make a group of wildly different people of different creeds and races come together for realistic reasons. You can just say that they are adventurers for hire, and Bob's your uncle.
- See here for a man who fights like a murderous hobo.