Naruto is the protagonist. This means that the story is about Naruto. As a protagonist, Naruto has a dream, and because he's a shounen protagonist in particular, he will believe in his dream and pursue it against all odds no matter what.
Naruto's dream originates from his disadvantaged beginnings. Naruto is the vessel of the nine-tailed fox (Kyubi), the demon monster that attacked Konoha village and was sealed inside Naruto when he was just a baby. The villagers who were around to remember the tale believe that Naruto is a liability to the village. They hope that he never becomes strong, and ostracize him as if he were the monster itself. Naruto has no idea why he is ostracized, but to prove that he's worth something, Naruto's childhood ambition is to become the greatest ninja the village has ever seen—the kind of ninja that can protect the village and earn the acknowledgment and respect of all the villagers. To achieve this, Naruto's aims to become Hokage and surpass all the previous Hokage.