The opening lines introduce the speaker and the people, "them," who will be the subject of his poem. He does not specify right away exactly who these people are—their identity will be developed over the course of the poem. Right away, however, the reader does know that there is a contrast between their dull "grey" surroundings and the "vivid faces" of the people the speaker encounters. They may be coming from their ordinary, everyday jobs at shops or offices, but on the inside, they have some unusually high degree of emotion or passion.
There is also a contrast drawn between these people and the speaker. The speaker does not seem to take their passion seriously. Rather than engaging with these people in a meaningful way, he simply "pass[es]" them with a mere nod or, if he must speak with them, only says "polite meaningless words." Whatever it is that animates these people, he does not wish to get involved with it. These contrasts—between the speaker and these people, between these people and their surroundings—prepare the reader for some conflict to arise later in the poem. The opening line foreshadows the result of this conflict by setting the poem at "close of day." At first, this phrase refers simply to evening, to night falling. But later in the poem, the speaker will use "nightfall" as an image of death. The speaker didn't know it at the time, but he was encountering these people near the close of their lives, shortly before their deaths.
The opening lines also introduce the poem's meter. The poem is written in a mix of trimeter and tetrameter, generally having three or four stressed syllables (beats) per line, but with an irregular number and varying placement of unstressed syllables. The first four lines, for example, scan this way:
I have met them at close of day (8 syllables)
Coming with vivid faces (7)
From counter or desk among grey (8)
Eighteenth-century houses. (7)
Lines 1 and 3 start with an unstressed syllable and end with a stressed syllable; lines 2 and 4 do the opposite. Line 1 begins with an anapest; line 3 begins with an iambic foot. Iambic feet are common in the poem, and the poem is fairly consistent with its three stressed syllables per line, but the unstressed syllables introduce considerable variety in the poem's overall rhythm and meter. This variation, besides adding interest to the pure sound of the poem, helps reflect the speaker's inner conflict about the people and events he is describing. He has difficulty deciding how to judge them, just as the poem seems to have difficulty deciding what exact rhythm to follow.