A lover of humanity, Walt Whitman feels that he is a part of everyone else as well as a part of Nature. So, when he writes "I celebrate myself," Whitman implies that he celebrates all mankind. Much like his contemporary Ralph Waldo Emerson, who wrote him and praised this work, Whitman felt himself a part of something similar to Emerson's concept of the Oversoul.
Like Emerson, Whitman believes that the individual human heart can embrace the entire universe. His "Song of Myself," therefore, is both an offering of himself and a celebration of this unity of self with nature and culture. "I am the poet of the woman the same as the man," he writes. In Section 16, also, Whitman writes of his connection to the world: "Of every hue and caste am I, of every rank and religion."
Further, Whitman's placing of himself in and out of the points of view of others reflects his commitment to democracy and equality. Thus, the reader of "Song of Myself" is able to view the world through the eyes of the poet, and, therefore, experience a sense of unity in humanity. In the final section (52), Whitman writes,
Failing to fetch me at first keep encouraged,
Missing me one place search another,
I stop somewhere waiting for you.
In Leaves of Grass the sensibilities in the individual as described throughout the poem by Whitman are actually linked to a larger social and political fabric. For this reason, then, the phrase "I celebrate myself" serves as an appropriate introduction.