When the poem begins, the speaker isn't doing well. Readers never learn what's going on, exactly (the speaker variously uses "sorrow," "grief," "want," and "pain" throughout the poem), but what matters is that the speaker is in a desperate situation and in need of help. The opening line's thudding alliteration ("deep distressed") sounds fittingly dramatic and urgent, capturing the speaker's dismal state.
Next, along comes a "proud man." He's clearly a wealthy individual, and most likely a member of the middle or upper class. "Proud" is an important word here, implying that this man is defined by his own sense of self-importance. He senses a vast societal difference between himself and the needy speaker.
Unsurprisingly, then, the proud man's response to the speaker lacks any warmth. He just gives the speaker a "cold" look and some "gold." Notice how this internal rhyme links the proud man's "cold" manner with the "gold" he gives, suggesting a connection between material wealth and apathy towards other human beings. The use of "gold"—as opposed to, say, "money"—also gives the poem a more timeless, allegorical feel (as though it is teaching a universal moral lesson, rather than talking about a specific situation).
The "proud man" then leaves without offering a single "kindly word" to the speaker. To this man, it seems, such kindness doesn't have any real value. Only "gold" does. To him, the speaker is just a problem to toss money at rather than an equal human being worthy of genuine consideration.
This opening quatrain establishes the poem's form. This stanza, like the ones that follow, uses something called common meter (a term sometimes used interchangeably with ballad meter). That means it follows an ABCB rhyme scheme and alternates between lines of iambic tetrameter and trimeter. An iamb is a poetic unit of two syllables, following an unstressed-stressed (da-DUM) beat pattern. Tetrameter just means there are four of these iambs (four da-DUMs) per line, for a total of eight syllables. Trimeter means there are three iambs:
I lay | in sor- | row, deep | distressed;
My grief | a proud | man heard;
His looks | were cold, | he gave | me gold,
But not | a kind- | ly word.
This meter/rhyme scheme lends itself well to music—and, indeed, this poem was in fact written to be sung! The regular rhythms and predictable rhymes make it easy to remember, which is no accident: the poem has a distinct moral lesson to teach, and the use of common meter makes this lesson more memorable.