In Whitman's preface to Leaves of Grass, he states the following: "The United States themselves are essentially the greatest poem. In the history of the earth hitherto the largest and most stirring appear tame and orderly to their ampler largeness and stir....the genius of the United States is...in the common people....the air they have of persons who never knew how it felt to stand in the presence of superiors." I'd like to use this section of the preface to consider the last part of your question—what a leaf of grass might mean to Whitman.

Expanding upon the answer above, there is something that resonates both in Whitman's preface to the work and in the poem at large about multitudinous individual entities functioning together to create a larger, more glorious whole. In Section 28 of "Song of Myself," the speaker observes those around him as "hardly different from myself." There are two things to call attention to here. First, the most relevant relationship between the speaker and those with whom he stands is similarity. He is a leaf of grass, just like every other leaf of grass around him. However, the speaker does call attention to the fact that there is difference, even though it's slight. This speaks to the uniqueness of each individual leaf. These two seemingly conflicting attributes— similarity and difference—in fact function in confluence to create the "greatest poem" that Whitman describes. Individually, we (Americans) are wild and fierce, but because we are all wild and fierce together, we appear "tame and orderly." Whitman finds beauty and power in this. The details that Whitman examines in this poem are essentially his thesis: that we are unrivaled because of the combination of our individuality and our unity.

Leaves of Grass is an ode to humanity, particularly an ode to America and its unique diversity. As the previous educator explained so beautifully, each "leaf" of grass is unique, given its own shape and size, but is rather unremarkable on its own. It is when that "leaf" becomes a part of a greater whole that it takes on a fuller shape and identity.

Whitman's decision to call his lengthy poem "Leaves of Grass" is a possible play on words. Yes, there is the allusion to the plant, to an individual "leaf," or blade, of grass. A leaf is the organ of a plant, providing it with nourishment. There is, thus, the suggestion that each of us nourishes—or, contributes something—to humanity. However, there is also the "leaf," or page, of a book. It is for you to decide what a "leaf" of grass means to you and what you think it meant to Whitman, based on what he describes in the poem.

In Section 31 of "Song of Myself," Whitman remarks on the extraordinary character of aspects of life we take for granted:

I believe a leaf of grass is no less than the journey-work of the stars, And the pismire [an ant] is equally perfect, and a grain of sand, and the egg of the wren...

These are the smallest things, the things we often forget to see. Whitman calls us to look at them, to see the way in which they can inspire as much wonder as the stars, for they are equally unique and intricate in their construction.

By the third line of the first stanza, he provides a list of other things that can inspire similar wonder: the tree-toad, the running blackberry, the hinge of his hand, the cow, and the mouse.

Today in America we would probably say “Blades of Grass,” but the metaphor speaks to the infinitude of things – stars, individual leaves, individual blades of grass, individual grains of sand, individual drops of rain or flakes of snow, and human individuals.  He recognized and understood the mature notion that, while each of us thinks of ourselves as a unique entity (and rightly so, since we have a “self” consciousness), we form together another entity, be it the starry night sky, the sandy beach, the vast grasslands of the prairie, the deluge of a river or ocean, the blizzard of a winter’s day. Whitman is saying “Our unique individuality is beautiful, useful, important, because together we make up the universe. We are 'leaves of grass.' In that sense we are like a star in the sky – a single manifestation of the fact of universal unity."  So, in describing his own life, he is sharing with us this unity, this marvelous facticity.