Shoes are hanging out to dry hanging on a line, they'll be polished by and by; shine, shoes, shine.
Shoes are walking down the street, walking on a line; dusty shoes on tired feet, shine, shoes, shine.
Two small scenes sit side by side here, both about shoes. In the first, they hang on a line, drying out and waiting to be polished. In the second, they're back on the street, walking, dusty and worn down by the feet inside them. The refrain, "shine, shoes, shine," ties the two together like a gentle chant, half a command and half a wish.
What the speaker feels is never stated outright, but the tone is quiet and a little tender. There's a sense of ordinary weariness: the phrase "tired feet" does a lot of work in just two words. The shoes stand in for a person's daily life, the routine of going out, getting dusty, being cleaned up, and going out again. The repeated "line" is a nice touch, too. Shoes hang on one line and walk on another, as if the day itself were a line to follow.
The mood is soft, rhythmic, and slightly melancholy, but hopeful. The poem seems to say that tiredness passes and things can be made bright again.