The V is a secret organization of ghouls, that operates in the shadows and strives to maintain a "balance". Because their so-called "balance" is collapsing due to Aogiri Tree, they are aiming to eliminate the One-Eyed Owl and One-Eyed King.
In the manga, Yoshimura, formerly known as Kuzen, was among one of their cleaners, individuals tasked with dispatching those that threaten the organization including human, ghouls, and rival organizations. He then met a human woman named Ukina, who he eventually fell in love with, and impregnated. Kuzen later found out that Ukina was a journalist who tried to chase after the organization. Then V discovered her identity and their relationship and Kuzen was ordered to assassinate her. Kuzen refused to do so, but after Ukina's pleading, he complied. Shortly afterwards, Kuzen defected from V, and out of fear for his child, abandoned her in the 24th Ward together with Ukina's diary, where she could be out of V's grasp. However, Kuzen's daughter would soon reappear, attacking CCG Headquarters, and out of fear for her becoming a target of V, Yoshimura took on her identity as the One-Eyed Owl, and began acting in her place. Just before the Anteiku raid happened, Kaiko and other members of V reappeared to offered Yoshimura redemption by giving up his daughter, but he declined. Being rejected, Kaiko told him to die and there was no escape for a bird in a cage like him.
It is unknown of what V's activity in present time.
In the anime, however, events played out differently. When V learned about Yoshimura's family and his betrayal, they tried to eliminated them. Kuzen fled together with his family, but Ukina was killed during their escape, and as last resort, Kuzen had to leave his child in an abandoned house. Shortly after Kuzen had successfully survived the V's attack, he return for his baby daughter but the child was taken away.