Short answers, pulled from the story.
The Lusus Troiae, or Troy Game, was an equestrian ceremony performed by boys of the Roman nobility. It featured three troops of twelve riders each who performed intricate interlocking drills on horseback as a display of communal skill, not a competition. It was staged at imperial funerals, temple dedications, and military victory celebrations.
Participation was restricted to boys of the nobility, known as nobiles, who were too young for military service. In 47 AD, Nero took part at the age of nine alongside Britannicus. The young Tiberius led a turma at the games on the 18th of August, 29 BC.
Julius Caesar revived the lusus Troiae in 45 or 46 BC, likely because his family claimed descent from Iulus, son of Aeneas, who appears as a rider in the Troy Game in Vergil's Aeneid. Augustus later established it as a regular event, making it a fixture of Julio-Claudian dynastic display.
Vergil provides the fullest description of the Troy Game in Aeneid book five, lines 545-603, setting it at anniversary games honoring Anchises. He depicts three troops wheeling, dipping lances, winding in and out of one another, and compares the patterns explicitly to the Cretan Labyrinth.
Vergil explicitly compared the equestrian drill to the Cretan Labyrinth, and scholars have interpreted the game as a form of initiation ritual representing a return from danger. A late seventh-century Etruscan wine-server from Tragliatella near Caere shows mounted youths emerging from a labyrinth inscribed with the word TRUIA, one meaning of which is Troy.
The Troy Game was performed at imperial funerals, temple foundings, and military victories, and was occasionally staged at the Saecular Games. Known performances include the dedication of the Temple of the Divine Julius in 29 BC, the Theater of Marcellus in 13 BC, and the Temple of Mars Ultor on the 1st of August, 2 BC.