Those who have achieved the title of Kage (影, Kage? literally "Shadow") are the leaders of the five most powerful Hidden Villages and generally the most powerful ninja in their respective villages. There may be exceptions, however; for example, a ninja may be the most powerful at the time of being installed as Kage, but he will age and a more youthful ninja may become more powerful.
A Kage may retire and give the title to someone else; the title, once granted, is held permanently. This creates a case where there are two Kage at the same time, with only one of them actually active -- as was with the Fourth Hokage and the Third Hokage, where the latter had given up the title to the former, only to come out of retirement when the former died.
The Kage stand equally with the rulers of their countries, oversee the activities of their villages, and are the leaders of ninja society.
The five Kage have different titles depending on their village. Those titles are:
Hokage (火影, literally "Fire Shadow"?) Kage of Konohagakure. Kazekage (風影, literally "Wind Shadow"?) Kage of Sunagakure. Mizukage (水影, literally "Water Shadow"?) Kage of Kirigakure. Raikage (雷影, literally "Lightning Shadow"?) Kage of Kumogakure. Tsuchikage (土影, literally "Earth Shadow"?) Kage of Iwagakure.