What is an anaphora and how is it used in Whitman's "Crossing Brooklyn Ferry"?

There are actually quite a few examples of anaphora in the poem. Let's take a look at one:

Others will enter the gates of the ferry, and cross from shore to shore; Others will watch the run of the flood-tide; Others will see the shipping of Manhattan north and west, and the heights of Brooklyn to the south and east; Others will see the islands large and small;

In poetry, Anaphora is the repetition of initial words or phrases in subsequent sentences. The passage above illustrates the use of anaphora because the word 'others' is repeated in every succeeding line. The repetition of 'others' lends an interesting rhythm to the stanza and illustrates the narrator's awareness of the ties that bind him to his fellow man, past and present. He is cognizant of the fact that his ties to the greater web of humanity are predicated on the certainty that everyone shares an intrinsic experience universal to all.

The others that are to follow me, the ties between me and them; The certainty of others—the life, love, sight, hearing of others.

Another example of anaphora in this poem would be:

Just as you feel when you look on the river and sky, so I felt; Just as any of you is one of a living crowd, I was one of a crowd; Just as you are refresh’d by the gladness of the river and the bright flow, I was refresh’d; Just as you stand and lean on the rail, yet hurry with the swift current, I stood, yet was hurried; Just as you look on the numberless masts of ships, and the thick-stem’d pipes of steamboats, I look’d.

The above is an example of anaphora because the word 'just' is repeated at the beginning of successive lines. Again, the repetition lends a rhythm to the stanza, mimicking the continuing march of humanity throughout all of history. By using the literary device of anaphora, the narrator is once more emphasizing his shared experience with his fellow travelers.

Look’d at the fine centrifugal spokes of light around the shape of my head in the sun-lit water, Look’d on the haze on the hills southward and southwestward, Look’d on the vapor as it flew in fleeces tinged with violet, Look’d toward the lower bay to notice the arriving ships,

Saw their approach, saw aboard those that were near me, Saw the white sails of schooners and sloops—saw the ships at anchor,

The sailors at work in the rigging, or out astride the spars, The round masts, the swinging motion of the hulls, the slender serpentine pennants, The large and small steamers in motion, the pilots in their pilot-houses, The white wake left by the passage, the quick tremulous whirl of the wheels, The flags of all nations, the falling of them at sun-set, The scallop-edged waves in the twilight, the ladled cups, the frolicsome crests and glistening, The stretch afar growing dimmer and dimmer, the gray walls of the granite store-houses by the docks, 

Above, the successive repetition of the words 'saw,' 'look'd,' and 'the' demonstrate the use of anaphora. Every 'the,' 'saw,' and 'look'd' precedes the description of some minute detail in the narrator's birds-eye view of the skyline. The poet once again uses the literary device of anaphora to emphasize the narrator's connection with all of humanity. Shared experiences and shared emotions across time underline the commonality universal to the human race.