ほどけた靴紐 literally means “an untied shoelace.” The song uses this vivid image as a metaphor for stopping to fix what has come undone before continuing toward the future, making it both memorable and emotionally meaningful.
"Plastic" by Janne Da Arc is a pep talk, and it doesn't pretend otherwise. The chorus says it straight: "傷ついてそしてつまずいて" (you get hurt, and you stumble) and "涙流して人は大人になれる" (you shed tears, and that's how people grow up). The idea is that pain is part of the route, and the singer keeps pointing at one image for it: "この丘を越え" (crossing over this hill), after which you come out "少し強くなれる" (able to be a little stronger).
The verses are the part I like most, because they get more specific. He asks you to shut your eyes, "瞳を閉じてみてよ" (try closing your eyes), and admits there's a past you want to forget, but also "素敵な想い出" (lovely memories) you couldn't forget if you tried. Then comes a small, practical line: "ほどけた靴紐締め直し" (retie your loosened shoelaces). Retying your shoes before you set off again is a lovely, ordinary picture of getting back up.
The second verse is more honest. He feels left behind as the seasons change, and worries that wanting to be strong has quietly turned into "ただの意地" (plain stubbornness). Real strength, he says, is "違う痛みも受け止める勇気" (the courage to accept other kinds of pain too), not just gritting your teeth. By the last chorus the comfort gets personal: "君は一人じゃないよ" (you're not alone), with someone right beside you to wipe away your tears. Sappy? A bit. It works anyway.
Learner tip: watch the て-form doing all the work here. "傷ついて", "つまずいて" and "流して" chain actions together like "and then... and then...", and "〜てみてよ" means "go on, try doing it."