As the previous educator noted, it is impossible to "briefly" summarize "Song of Myself." Any summary offered to you will fail to cover every aspect of the poem. It would be better to summarize a cluster of stanzas, but, even then, sometimes Whitman shifts topics from one stanza to the next.
In addition to the massive poem being a celebration of life, it was also, according to Whitman scholar Ed Folsom, Whitman's idealistic attempt to use a poem to stop the impending Civil War. "Song of Myself" was first published in 1855, at the height of sectarian tensions, inflamed by the Compromise of 1850, which included the new Fugitive Slave Act of 1850. The new law demanded that slaves who escaped to the North had to be returned to their Southern plantations. Whitman included a narrative about aiding a fugitive slave, but also included among his vignettes of American life images of black men working and "a quadroon" being sold on an auction block. Whitman's images convey an ambivalence about slavery that may have been the nation's general attitude toward the peculiar institution at the time.
Whitman includes and validates people from every region of the country, despite being a New Yorker himself. He emphasized the beauty and value of every portion of the nation, including newly formed states, such as California and Texas, eschewing the sectionalism that was characteristic of the country at the time (and, arguably, now). Thus, one summary of the poem is that it is a celebration of a great, but troubled, nation.