The myth tells that Evadne, who was the daughter of Poseidon, had a son with Apollo, of which she was ashamed, and therefore she abandoned him to her fate. But the boy survived thanks to two snakes feeding him honey, until someone found him lying among violets and gave him the name Yamo.
When he was older he plunged into the waters of the river Alphaeus and invoked his father, Apollo, who ordered him to go to Olympia and granted him the gift of prophecy. Yamo founded in Elis, where ancient Olympia is located, a family of diviner priests, the Yámidas.
These Yámidas had divinatory skills so much in demand that other Greek cities often took them away, in exchange for important emoluments, in order to have a suitable fortuneteller. But the Yámidas also had another function, because since the 50th Olympiad (580 BC) one of the two judges in charge of organizing the Olympic Games was chosen from among them. They were called agonothetai (organizers).
Some 180 years later, during the 95th Olympiad (400 BC), the number of organizers and judges was increased to 9, and they were called Hellanodic (literally judges of the Greeks ), which is the term that would last in successive extensions.
The duty of the Hellanodics (in Greek Ἑλλανοδίκαι, Hellanodikai ) was, therefore, to organize the games, but also to ensure that the rules were met and that the competitions always had the highest level.
They were selected from among the inhabitants of Elis, the principal city of Elis in the northwest of the Peloponnese, a region in which the sanctuary of Olympia was located.
During the ten months prior to the celebration of the games, the Hellanodics lived together in a building near the gymnasiums where the athletes trained, called helanodiceo (and that it was located, according to Pausanias, higher than the tomb of Achilles ). There the nomophylakes (guardians of the law) taught them everything they needed to know about the rules and regulations of the different disciplines of the games, so that they could perform their duties properly.
Although they were the organizers, referees and judges of the games, they could also compete in them (which today would seem nonsense), until in the 102nd Olympiad (around 372 BC) it seems that they were prohibited, according to Pausanias: 
During the last month before the games, they were in charge of selecting the athletes who were going to participate, choosing those whose performance, considering aspects such as power, resistance or speed, was more satisfactory. But also giving great importance to behavior, character and morality. And, obviously, ensuring that all of them were authentic Greeks (as happened to Alexander I of Macedonia around 500 BC).
Those selected were registered in the leukoma , the list of participants, and two days before the start of the games they headed from Elis to Olympia, in a procession led by the Hellanodics. And on the opening day of those, they went back in procession, this time to the stadium, which they entered through a hidden door, probably a tunnel located in the northwest corner.
They wore purple robes and had their seats on a platform on the south side of the stadium. Three of the Hellanodics supervised the pentathlon, three the equestrian competitions, and another three the rest of the tests. The oldest of them acted as general supervisor. And, of course, they gave the crowns and palms to the winners, except in case of a tie in which the crowns were offered to Zeus.
But what if a Hellanodic was wrong, say, on purpose? Well, there was an Olympic council that athletes could turn to. This council could not amend or change the decisions of the Hellanodics, but it could punish them if necessary.
There were several occasions when the Hellanodics were involved in controversy. Pausanias mentions the case of Eupolemus of Elis, whom two of the judges declared the winner in the race, while the third Helanódica declared Leon de Ambracia the winner.
Leon appealed to the Olympian council and got the two Hellanodics punished, suggesting that he was the fair winner.
But perhaps the biggest scandal they were involved in was when they supposedly accepted a million sesterces from Nero to allow him to compete, and win six trials, in the games of 67 AD. (which were to have been held in AD 65, but were also postponed at the behest of Nero). According to Pausanias, the Olympics of that year were the only ones omitted in the logs.
In any case, during the more than a thousand years in which the Olympic Games were held in ancient times (from 776 BC to 393 AD), the Hellanodics more than fulfilled their mission of organizing and ensuring compliance with the rules. They were held in high esteem among all Greeks and were always reputed to be impartial, despite the fact that their own compatriots also competed. Let's not forget that after all they were ordinary citizens, chosen by lottery.
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Description of Greece (Pausanias) / History (Herodotus) / Onward to the Olympics:Historical perspectives on the Olympic Games (Gerald P. Schaus, Stephen R. Wenn, eds.) / Ancient Olympics / A Companion to Sport and Spectacle in Greek and Roman Antiquity (Paul Christesen, Donald G. Kyle) / Wikipedia.