Tertius was the first wizard to use the potion Felix Felicis, or liquid luck (BoP).
Tertius was a Muggleborn, and after his parents died, his Muggle brothers feared his magical powers, so they broke his wand and threw him out of the house, where he fell into the sea. He washed ashore on the island of Hermetray, home of legendary Potioneer Zygmunt Budge, who nursed him back to health. The reclusive hermit also wanted Tertius to leave the island immediately, so he gave him money, a cloak, and a bottle of Felix Felicis, which he had just invented (BoP).
Thanks to Felix Felicis, Tertius luckily met a Wizarding family who invited him to travel to Diagon Alley. There he found a bag of gold lying in a gutter, and bought himself a new wand and robes. He also found a job at Gringotts, where he became one of the most famous curse-breakers ever (BoP).
Zygmunt Budge took revenge on the Muggle brothers of Tertius, sending them a bottle of "extra-strength" Shrinking Solution. They became the size of mice, and spent several days hiding under a cupboard from the family cat (BoP).
Tertius means "third" in Latin - probably referring to his place as a third child, since he had two brothers.