Finally, Whitman says that it's time to explain himself. (Wait a minute! What has he been doing all this time, if not explaining himself?)
The last section addressed the time of death, and this section addresses eternity.
He explains eternity as "trillions" of seasons that have passed and are yet to come. His point is that things have continued in a certain way for a long time, and they will continue in a certain way for a long time to come.
Everyone is equal in the face of eternity.
He feels bad for anyone who has been treated poorly by humanity, but he doesn't believe that humanity is naturally wicked or worth lamenting. The word "lamentation" suggests the Book of Lamentations from the Old Testament of the Bible. The Old Testament frequently depicts humankind's wickedness.
He sees a pattern of progress in the universe, and he's at the top. Below him he sees death. He believes he has been through death before and was carried through it by God.
The whole world – all the stars and dinosaurs ("sauroids" – awesome word) and forces of nature – has been preparing for Walt Whitman to "stand on this spot with [his] Soul."