The Hokage (literally meaning "Fire Shadow") are the leaders of Konohagakure. They are generally the strongest in the village, although ideology and renown plays a large part in their being chosen for the position. Four shinobi and one kunoichi have gained this title so far.
The Founding Hokage (literally meaning "Founding Fire Shadow") are the secondary leaders of Konohagakure. They are rumored to be an equal or sometimes stronger than the current Hokage. This is a position within Konoha that was created by the First Hokage, that was reown to be a secondary leader whether or not the current Hokage's alive. Three shinobi have gained this title so far.
Generally, the new Hokage is selected by the old Hokage on their retirement, but if the old Hokage dies or is incapacitated before being able to do so, the Konoha council and Fire Feudal Lord council will meet and appoint a new Hokage together - sometimes within hours of the former Hokage's death. Afterwards, the candidate Hokage will need to be approved by the jonin of the village. After being appointed, they are given the Hokage Mansion to live in and have their faces carved out in the moument behind it. If the former Hokage is still alive, they will keep helping out, making the transition easier and more stable. The Hokage carry their title for life, even after retiring from active duty.
List of Hokage
Real Name: Hashirama Senju
Hashirama Senju was a legendary ninja who became the First Hokage ("Shodai Hokage"; meaning the "First or Founding Fire Shadow"). He helped create Konohagakure along with his younger brother, Tobirama, and the Uchiha Clan. The father of Hanaku Senju, the hushand of Mito Uzumaki, and the founder of the "Will of Fire".
Founding First Hokage
Real Name: Hanaku Senju
Hanaku Senju was a legendary jinchuriki that became the Founding First Hokage ("Rikkoku Shodai Hokage"; literally meaning the "Founding First Fire Shadow"). He ended the First Great Ninja War with the original Shinobi Alliance with Kirigakure, Iwagakure, Kumogakure, and Sunagakure. He was the leader of the Senju Clan (after his father, the First Hokage's death), the son of Hashirama Senju and Mito Uzumaki, he was the fourth jinchuriki of the Chikaku, the Ten-Tailed Badger and was called the "Hero of the Leaf" and the Savior of the Worlds.
Real Name: Tobirama Senju
Tobirama Senju was a legendary ninja that became the Second Hokage ("Nidaime Hokage"; literally meaning the "Second Fire Shadow"). He hails from the Senju clan, who along with the Uchiha clan, founded Konohagakure.
Founding Second Hokage
Real Name: Sazaku Uchiha
Sazaku Uchiha was a legendary jinchuriki who became the Founding Second Hokage (Rikkoku Nidaime Hokage; literally meaning "Founding Second Fire Shadow"). He was the leader of the Uchiha Clan (after his mother and precursor, Otoka Uchiha) and became the first Uchiha to be called the "Master of the Mangekyo Sharingan" and was known the "Static Flame of the Leaf".
Real Name: Hiruzen Sarutobi
Hiruzen Sarutobi is revered as the "God of Shinobi", was a legendary ninja who became the Third Hokage (Sandaime Hokage; literally meaning "Third Fire Shadow"). He hailed from the Sarutobi Clan of Konohagakure. He was part of Team Tobirama together with Homura Mitokado and Koharu Utatane under the leadership of the Second Hokage. He was also trained by the First Hokage and would later become the teacher of the second generation of the Legendary Sannin: Jiraiya, Tsunade Senju, and Orochimaru.
Founding Third Hokage
Real Name: Nagiren Denshiko
Real Name: Minato Namikaze
Minato Namikaze, also known as the "Yellow Flash of the Leaf", was a legendary ninja who became the Fourth Hokage (Yondaime Hokage; literally meaning "Fourth Fire Shadow").
Founding Fourth Hokage
Real Name: Vacant; Not Decided Yet!
EIther the Fourth Hokage, Fifth Hokage, Konoha council, and Land of FIre council with the Fire Fedual Lord haven't decided the Founding Fourth Hokage who is an equal or greater than the Fourth Hokage.
Real Name: Tsunade Senju
Tsunade Senju is a legendary kunoichi who became the Fifth Hokage (Godaime Hokage; literally meaning "Fifth Fire Shadow"). who is a member from the Senju Clan of Konohagakure and is also a descendant of the Uzumaki Clan through her grandmother Mito Uzumaki. She succeeded the position after the death of her teacher, Hiruzen Sarutobi. She, along with Orochimaru and Jiraiya, are the second generation and recognized as "The Legendary Sannin of the Leaf".