TL;DR #
aria‑label, aria‑labelledby, and aria‑describedby can all be used to bring extra clarity to a given element when it's exposed to assistive technology.

aria‑label overrides an element's name with contents you specify.
aria‑labelledby replaces an element's name with contents from another node on the page. You'd use this when you'd already have a visible label anyways.
aria‑describedby sets your element's description to the contents of another node on the page. This is great for noncritical, supplemental information.