1To polish, scrub, or shine a surface (e.g. brush teeth, polish shoes, clean a lens).
毎晩、歯を磨く。
I brush my teeth every night.
母は靴をきれいに磨いた。
My mother polished the shoes until they were clean.
レンズの表面を柔らかい布で磨いてください。
Please polish the surface of the lens with a soft cloth.
2To refine or improve skills, abilities, or character; to hone or cultivate something intangible.
日本語の発音を磨くために毎日練習している。
I practice every day to improve my Japanese pronunciation.
彼はピアノの技術をさらに磨いた。
He further refined his piano technique.
社会人としての教養を磨くことも大切だ。
It's also important to cultivate one's refinement as a working adult.