Poem found here: "A Glimpse" by Walt Whitman
Do you know those scenes in Romantic movies where time slows down, the music stops, and then our couple looks in each other's eyes and the connection is there. Well that's what is portrayed. The overall feel of this poem is that moment. However, the speaker admits this moment through the title itself, "a glimpse" who is the one peeking
"A glimpse, through an interstice caught, / of a crowd of workmen and drivers in a bar-room, around the stove." Note how the poem starts on the outside and focuses in. Here the crowd is of "workmen and drivers," innocuous enough, but also note that this is in a bar-room, "late of a winter night -- and I unremark'd seated in a corner;" in which it is cold and the speaker separates himself from the others.
But the semi-colon of the line connects his need to be alone with, "Of a youth who loves me, and whom I love, silently approaching, and / seating himself near, that he may hold me by the hand;" Now there's the romantic moment of holding hands. That silent approach. That admission of love.
Who has a glimpse of this? On one aspect, it is the speaker who is looking through the crowd to see his love, But there is also the reader. Remember that the workmen and the drivers are part of the scenery, but it is the reader who is viewing this scene -- interpreting it. And how the speaker tries to give meaning to every gesture and every moment for himself and also for those who glimpse with him.
"A long while, amid the noises of coming and going--of drinking and / oath and smutty jest." The scene returns to it's bar-room antics. The noises come back and the people are there. Do these things apply to the couple? The speaker differentiates this moment with what is there, "There we two, content, happy in being together, speaking little, / perhaps not a word." Note the silence that repeats throughout the entire poem -- the silent approach, the silent being.