We really aren't particularly sure. Our textual material disagrees on whether it was originally an Etruscan custom or whether it was an import from south Italy. That the gladiatorial contests were a foreign custom is regularly attested and was considered obvious by Romans. In general, the Romans believed that it was an Etruscan custom first, which is what our first attested source states. Unfortunately, that source, Nicolaus of Damascus, is almost completely lost, and we're not really sure how accurate his works were.

Most scholars were of the opinion until only a short time ago that the gladiatorial contests were an Etruscan burial ritual, which is attested by our source material and by the evidence found in Etruscan tomb-frescoes, which often portray combatants in single combat, frequently equipped like gladiators later. The generally accepted theory is that it was a sort of blood-rite that was used to appease the shades of the dead, which fits neatly in with our predominating theories on Etruscan religious beliefs. It's highly debated whether the Etruscans believed that the afterlife was kind of a party or whether they thought it was this grim place of punishment and sorrow, but what is certain is that the shades of the dead could be very much present in the physical world and could cause a lot of trouble if left unappeased. If the gladiatorial contests are an Etruscan rite then they must have been brought to Rome sometime during the 5th or 4th Centuries, when the Etruscan presence in Rome was large. A later date doesn't seem to make much sense, unless the custom was adopted following the conquest of Etruria, which is possible

Livy, however, gives us a completely different picture. Livy claims that the first gladiatorial pair fought in Campania in honor of the Campanians' victory over the Samnites in 310, B.C. According to Livy (who is the only source who mentions the custom's actual introduction at Rome, rather than just its origins) the custom was brought to Rome in 264, B.C., when three pairs fought to the death as part of the funeral rites of Brutus Pera.

It's very difficult for us to tell where exactly the custom originated. Recent work in the Greek cities of Campania have revealed tomb-frescoes similar to those in Etruria, with single fighters paired off against each other. These frescoes are actually somewhat earlier than the Etruscan frescoes depicting duelists (some time during the 4th Century), but our sources insist that the Etruscans were performing blood rites by combat since their earliest intrusion. It's probable that the custom was introduced to Italy either in Etruria or Campania, and then was spread to the other location very quickly, since the Etruscan cities had close ties with the Greek cities of Campania, particularly Paestum and Cumae. In the historical period it was certainly closely associated with Campania, where most of the gladiatorial schools were located and where most of the best gladiators came from. What is known is that the rite took a long time to take off in Rome. From it's introduction during the First Punic War to Caesar's great games in 65, B.C. in honor of his father (really to prove that he was an awesome aedile) there are only a handful of games mentioned, although it's certain that private individuals all over Italy were holding smaller combats in honor of their dead, a custom attested frequently later on. The gladiatorial schools by then were quite large (large enough that Spartacus' revolt was dangerous even in its early stages, before other slaves, peasants, and unsatisfied southern Italian allies joined him) but state-sponsored games were a rarity.

Here's something important to note. No matter where exactly the gladiatorial rites originated, they were sacrificial in nature. Livy, who like most Romans following the Punic Wars is disgusted by the thought of human sacrifice, tries to sugar-coat this, which is something he does all throughout the Punic Wars, when it's quite clear that the Romans were sacrificing people quite regularly during their major times of crisis. The gladiatorial combats were sacrifices to appease the shades of the dead, and to offer thanks for great victories. Offer thanks? What? In Greece, and elsewhere, it was common to dedicate an offering of the spoils of battle to some god following a great victory. This was usually made in the form of arms and armor captured in battle. But most peoples originally dedicated captives as well, something that first appears in Egyptian records from the predynastic period, and which is well-attested in Sumer, Babylon, Assyria, Canaan, Persia, early Greece, the Indus, Celtic peoples...the list goes on and on. Usually those mass slaughters of captives disappear fairly early on (although the Egyptians were doing it for thousands of years). In Greece they were replaced extremely early by dedications of armor, and only survive as a dim memory in myths and in traces remaining in Homer. In Rome...they actually stuck around for a really long time. They were rarely used, except after a great struggle or to show off, but we find them as late as Caesar's triumph over the Gauls an it's possible that there may have been a massacre of Dacian captives during Trajan's triumph. Well, the earliest attested gladiatorial rites are basically sacrificial combats between captives. Livy notes that they were mainly during the Samnite Wars and following Roman reconquest in Samnium and southern Italy, after Hannibal had raised hell down there. Livy claims that the Samnites adorned themselves in showy armor which the Campanians detested. As a result, they dressed their gladiators in Samnite armor. Yeah...no. It's quite obvious that the gladiatorial combats staged by the Campanians that Livy mentions were a ritual slaughter of captives by single combat. It's a custom seen elsewhere in the Indo-European world, but never on such a scale. Another obvious example of early gladiatorial combats as ritual sacrifices is Scipio Africanus' games following the end of the Second Punic War. These were ostensibly in honor of his relatives who had died during the war, but that wasn't the only reason. Since they were linked to the defeat at Cannae they were an appeasement to those shades, as well as a thanks for ultimate military victory and the religious purification of the state from the disaster.

So it's rather complicated and we're not entirely sure.

The first gladiatorial games in Rome were part of the funeral of Junius Brutus in 264 BCE. Though the use of gladiators was novel, the concept of such a display was not --- funeral games, such as chariot races, were performed as a way of showing respect for the dead. At this time, the family of the deceased was responsible for the cost associated with these rites.

Like chariot races, gladiatorial games grew to be wildly popular. These entertainments were presented with increasing frequency and were no longer limited to funerals. Massive structures were built to accommodate the tens of thousands that flocked to every show. The financial burden shifted to those with political aspirations, who sponsored games in the hopes of bettering their public image or swaying voters in an upcoming election. These sponsors were held in high esteem, so much so that after the reign of Domitian, the emperor became the sole sponsor of the games.