Cecelia was Pegasus' childhood sweetheart—they met at a party thrown by his businessman father in Las Vegas about fourteen years before Duelist Kingdom. He was an artist back then, constantly sketching her. They got married young, but she died of a disease shortly after at just seventeen years old.
Her death obsessed him. Pegasus became determined to find a way to bring her back, which is what drove him to seek out the Millennium Eye from Shadi in the first place. His whole motivation for putting Yugi and his friends through hell to take over Kaiba Corp? He needed the company's resources to create a hologram of Cecelia. In the English version, it's framed even more dramatically—he wanted to combine the Millennium Items' power with Kaiba Corp's holographic technology to actually resurrect her.
Yugi and the gang eventually figured out the truth after discovering Pegasus' diary, which laid bare everything he was feeling. It recontextualized a lot of his cruelty—he wasn't just some power-hungry villain, but a grieving husband willing to cross every line for the woman he lost.
Content compiled by AnimeList.moe from publicly available sources.