"The Worldstone has been changed. Our children are born weak and suffer short lives. The demon Nereza promised to restore their power but instead turned them into misshapen creatures and sent them to war against us. We may die, but not before she is sent back to the Burning Hells."— Alaric(src)
A nephalem, Alaric was active during the early days of Sanctuary, after Inarius had altered the Worldstone to diminish the nephalem's abilities. As a result, the nephalem's children were born weak with short lifespans. Alaric and his kin turned to the demon Neraza, who promised to restore their power. Instead, she turned them into her servants and sent them to war against Alaric and his followers. The battle took place near the Drowned Temple. Even in death, reduced to ghosts, Alaric and his kin continued to wage war.
"Are you nephalem?"— Alaric and Leah(src)
"No. There have been no nephalem for a millenium."
"Huh. Another myth."
Thousands of years after the Sin War, Alaric maintained his guardianship over the Drowned Temple. It was here that he was eventually visited by Leah and the Nephalem, who sought to enter the temple to retrieve the second shard of the sword El'druin, a shard of which has awakened the ancient Nephalem spirits, driving them to madness. Amused at Leah's ignorance of his kind and (surprisingly) untouched by the sword's effects, Alaric told them that only a nephalem could enter the temple, but told the group to fetch keys to enter the temple from its outlying tombs. The heroes succeeded, and Alaric directed them to enter the tomb and defeat his fellow guardians.
The heroes succeeded, and Alaric commented that the Nephalem's strength rivaled that of their greatest champions, realizing that the hero(es) was/were indeed nephalem, even if they didn't know it. Regardless, he granted the group access to the temple's most sacred ground, where they were able to retrieve the shard they sought.
Later in game, Leah may ask The Nephalem about if they think it is true. In various forms, all six classes reply that, with all due respect, Alaric must be mistaken. Ironically, it was Alaric who has given this title to the heroes, and most in-game characters address to the Nephalem subsequently.