A mercenary is a warrior who fights for money, without concern for loyalty to national or ethnic identity. Long before standing armies, mercenaries would sell their services to the highest bidder, becoming valued professional soldiers.
In medieval times, mercenary companies were extremely common. These soldiers would be hired as a complete unit, and fielded as such. The Genoese crossbowmen at the Battle of Crecy were such, as were the late-medieval Italian condotteri (literally "contractors").
Other examples of medieval mercenary companies included the Varangian Guard of Constantiople and so-called free-lancers: mounted horsemen with no fealty to a specific lord, literally a "free lance" who could be hired into service.
In period they were used to supplement (or substitute for) a kingdom's army -- their main drawback lay in the fact that, once the principle of fighting for money had been established, it was not long before the concept came along of changing sides in return for more money.
At one stage medieval Europe was lousy with mercenary companies, led by the like of Sir John Hawkwood or Roger di Flor, who had elevated their art from fighting for money (and spoils) to not despoiling a territory if they were given enough money to go elsewhere (qv Danegeld)
While highly sought after as skilled and disciplined warriors, they were often reviled as being honorless hirelings. Mercenaries' value was increased by the fact that the feudal rule of "forty days' military service" did not apply to them: they would be obliged to fight as long as they continued to be paid.
Most modern mercenaries are more like security consultants than combatants. The notion of a mercenary company along medieval lines is extinct, except for one notable exception: the Swiss Guards of the Vatican are still a mercenary company along medieval lines. However, the terms of their contract is extremely long-term, and not likely to change anytime soon.
Mercenaries in the SCA
The romantic image of the "Soldier of Fortune" has spawned many mercenary households in the SCA, such as Iron Lance, Concusare, and Perchainne. Usually these households are hired by the crown or other nobles for war events such as Pennsic. Under such circumstances, mercenaries are usually paid in useful goods (rattan, armour, fabric), SCA currency and beer.
There are some households known as "Allied" households, who are not tied to a specific Kingdom but are also not "hired" in any way. This can be for many reasons, such as having a nomadic household persona, having members in more than one Kingdom who would like to fight as a unit, or being from a non-SCA organization that occassionally participates in the SCA on masse at events like the Pennsic War. They may make an alliance with a given Kingdom for the term of a war event or a reign but are not paid for it, and are not considered mercenaries. Some examples of Allied households include the Great Dark Horde, the Rozakii, and the Tuchuks.