The speaker launches into this poem with an exasperated outburst: "O me! O life!"
Right off the bat, the reader might find something a little odd in the exclamation "O me!" This now-unusual expression was once a common lament, along the lines of "Aw, man!" It turns up in Shakespeare, for instance, when Juliet is sighing on her balcony. But by the time Whitman was writing in the 19th century, this turn of phrase (technically an example of apostrophe) would already have felt old-fashioned.
That dramatic "O" makes the speaker's outburst feel even more loaded. "O" is a grand word, the kind of word one would use to address a goddess (as Keats does in his "Ode to Psyche," for instance). There's something big and serious going on here, then, not just a minor complaint. This speaker is having powerful feelings, grappling with something difficult.
That serious thing might be both "me"—the speaker's self—and "life" in general. For it's "the questions of these" that "recur[]" to the speaker, repeating themselves over and over. In other words, not only does this speaker have big questions, those questions don't seem to have clear answers: the poor speaker has to ask them again and again, struggling with a mystery.
Much of the rest of this free verse poem will investigate that mystery in rhythmic, free-form lines.