This poem is pretty much what the title states it is; it is Whitman writing a poem in which he sings the praises of himself, of his life, of the life that surrounds him, and of the sheer beauty and joy that it is to be himself at this point in time. It is a joyous, thrilling ode to life. In section one, he focuses on how he feels blessed to be who he is. He states, "I celebrate myself and sing myself," to indicate this section will be about rejoicing in who he is. He goes on to state that he feels so great about himself right now that whatever he believes ("assumes"), everyone else should believe too, because, he says, we are all made of the same stuff ("atoms") and so are all one; because we are all one, we should rejoice the same.
He states that he finally begins to rejoice, being made of the same stuff that his parents and their parents were made of, and that at age 37, he feels ready to feel joy and not stop until death. He states that he puts all of his previous learning behind him ("creeds and schools at abeyance") and starts new; he will accept all that life gives him, for good or bad, and speak of the beauties of all of it. He compares this approach to "nature without check with original energy," meaning, like nature, good and bad happens, but it is all energetic and beautiful.
I hope that summary helps interpret that poem a bit for you; good luck!