Does this mean that the Prophet, peace and blessings be upon him, would seek Allah's forgiveness and repent to Him a hundred times every day?

What you heard about the Messenger of Allah, peace and blessings be upon him, is correct. It has been narrated in Sahih Muslim and other collections that he said: "O people, repent to Allah and seek His forgiveness, for I repent to Him one hundred times a day." It was also narrated from Ibn Umar that the Prophet, peace and blessings be upon him, used to say: "O Allah, forgive me and accept my repentance, for You are the Most Forgiving, the Most Merciful," one hundred times. Seeking forgiveness means saying: "I seek forgiveness from Allah and I repent to Him." Scholars have interpreted his seeking forgiveness as a demonstration of servitude and humility, or as a teaching for his Ummah, or for leaving what was better, or out of humility, or because whenever he ascended a degree in closeness [to Allah], he sought forgiveness for the previous one.