Mokuba is Kaiba’s younger brother and his only surviving family. Their mother died giving birth to Mokuba, and their father died in a car crash when he was only three. None of their relatives would adopt them, so he and Seto went to live in an orphanage for years. Many couples wanted to adopt Seto, but he refused to leave his younger brother behind. Eventually, Kaiba Gozabaro took them both in when Seto managed to beat him in a chess match.
Mokuba hero worships his older brother, and believes he can do nothing wrong. (Though that view does somewhat change over time). It was quite a shock to both Kaiba brothers when Yami Yugi managed to beat Kaiba in Magic and Wizards (a.k.a. Duel Monsters in the anime world). Mokuba challenged Yami Yugi to a game of Capsule Monsters, and he cheated so he would get stronger pieces than him. However, the Game King still wins, and punishes Mokuba by mentally trapping him in a capsule to “think things over”. Later on, Mokuba reforms and become friends with Yugi and the rest.
Seto is the last surviving member of Mokuba’s family. Their mother died giving birth to Mokuba and then their father died five years after that. He was adopted by Kaiba Gozaburo along with Seto.