Private Military Contractors (PMC) are mercenaries, soldiers and other combatants employed by a private company or other organization and fighting on behalf of clients. While such soldiers of fortune are regarded with wariness in most settings, they're generally considered distinct from criminal enforcers, mafia hit men, and the like. The polar opposite of conscripts.
In the real world, they are usually ex-soldiers with decent to slightly-above-average equipment from the United States — the largest company, and largest number of companies, are American. Other common national backgrounds are former Soviet Republics or South Africa. Of course, there are plenty of less professional and less affluent outfits out there, some of which will hire just about anyone who'll take them up on their offer. It's a great summer job! In fiction, though, they tend to get all the latest and most expensive vehicles and support equipment as well, and are often recruited and trained by the company itself. Fictional mercenary groups often hire unique individuals or groups of various special types of fighters: ninja, ronin samurai, dishonored knights, mages, shapeshifters, and left-over warriors of defeated organizations, nations, or races that need to make ends meet. Some PMCs are just a Ragtag Bunch of Misfits.
These characters can be depicted as anything from heroic to villainous; in a conflict, they usually are allied with the richest party's faction, but sometimes have a strict honor code that prevents them from switching sides mid-battle. If they get tooenthusiastic about their job, they may become Blood Knights and try to start a War for Fun and Profit. On the other hand, they do have to deal with the risk of their employers double-crossing them when the job's done. And if their clients run out of money before the fighting's done, things will get ugly in short order in one or more of many ways.
In recent years, there's come to be a distinction between a "mercenary company" and "corporate mercenaries", especially in Western (American) television and movies. The traditional mercenary who hires himself out (or himself and a dozen of his best buddies) is seen as somewhat honest, with at least a personal code of honor of some kind (even if it's just "do the job, get paid"); determined to accomplish the mission for which he has been paid and takes his reputation very seriously; and is scrappy yet skilled. This character is usually played moderately sympathetic, or at least as an antihero. They will typically have some attention given to their, quite possibly colorful, personalities.
In stark contrast, the "corporate mercenary" is usually just a Mook or Red Shirt of some kind, and the "character" takes the form of the PMC corporation itself. Corporate mercs are usually depicted as being up to no good, or are the hand-puppets of some shadowy organization which is itself up to no good. They are portrayed — when anything more than Faceless Goons — as amoral, ethically-challenged, and professional but hardly ever inclined to argue with Corporate Headquarters. If former military, many will have been dishonorably discharged. Unless the writer's bent on defying What Measure Is a Mook?, they will almost never be the "good guys" in recent years. Their parent company usually has a name based loosely or thematically on "Blackwater" in a No Celebrities Were Harmed Expy of that real-life PMC — examples include "Blackriver", "Red River", "Blackthorne", "Murkywater", "Starkwood", "Bluewater", and "Belltower".
Note that although this trope description uses the terms "PMC" and "mercenaries" interchangeably, in Real Life the distinction between them is extremely Serious Business. This is because the international treaties that establish The Laws and Customs of War explicitly forbid the usage of mercenaries in warfare. While traditional mercenaries might be tolerated in practice,legally they are neither lawful combatants, nor non-combatants, and thus aren't eligible for protection and respectful treatment under, for example, the Geneva conventions. When captured, they are treated as a criminal gang at best, and at worst as complete outlaws.
Private military contractors are the way that some people try to weasel out of this ban on mercenaries. Even though the largest of these companies employ materiel that is ordinarily associated purely with the military — armor, helicopters, light warships — on paper, they are just your garden variety mall guards writ large, and they are not authorized to wage war on their own. Officially, these units may be employed only in some duties not involving actively engaging the enemy (though they can do this if forced), such as escorting convoys and guarding some civilian structures. In practice this mandate could be, and often is interpreted very broadly — "While you're on patrol, don't go and get into a fight with the insurgents at yonder hill three klicks to the southwest, but if they fire first, or if you see anything indicating a possible threat, then by all means, do whatever you must." Note that not all PMCs necessarily are thinly disguised mercenaries; a private military contractor is any non-government organization contracted by the military, which may include as mundane things as a contract to make and serve food for an army in peacetime.
Real Life PMCs run the gamut from dirty-working Hired Guns outfits to highly-scrupled organizations with very strict rules about what they will and won't do, and for whom. Some PMCs provide armed security for Christian (and occasionally Muslim) charities in war-torn regions like Darfur (the contractors who do this kind of work often give their clients a discount rate—it's charity, after all). Others patrol African elephant habitats hunting heavily-armed ivory poachers. Even those who take corporate contracts are much more likely to be doing "rent-a-cop" work making sure nobody blows up a pipeline than "massacre uncooperative village" jobs (although that does sometimes happen). Some PMCs are good people doing good work for good reasons (and making a living doing it). Others are willing to work for drug cartels. It is a very large and diverse category that probably shouldn't be painted with a broad brush, good or bad.
A PMC can provide a villainous Evil Army if one doesn't actually want to insult any real country's Armed Forces. If they're too much of an army, then they are an N.G.O. Superpower.
Mercenaries are the basic, land-based version of this trope; at sea and in space, they're privateers operating under letters of marque.
A sub-trope of Hired Guns, and can overlap somewhat with the Professional Killer. If employed by a Mega Corp., then Corporate Warfare can be expected. Commonly a favorite industry of a Proud Warrior Race.
Compare with Murder, Inc., a completely criminal enterprise devoted to assassinating selected targets, compared to the quasi-legal PMC. Compare & contrast with Pinkerton Detective.