Desmond Miles is the Animus user connecting the modern-day story in the first Assassin's Creed game.
Desmond is a descendant of several important historical Assassins, including Altaïr and Ezio. Abstergo Industries uses the Animus to access his genetic memories, beginning with Altaïr's experiences during the Third Crusade. Desmond's perspective provides the modern framework around those historical sequences.
The Animus is a fictional machine that allows a person to relive ancestral memories encoded in DNA. In the first game, the modern-day sections reveal that Abstergo's research has a larger purpose than ordinary historical study.
William Miles is Desmond's father and a senior Assassin, not the first game's Animus subject. Layla Hassan becomes the modern protagonist much later, beginning with Assassin's Creed Origins. Desmond remains central to the early modern-day arc across multiple games.