My mother looks younger than her age.

Literal

Mother [topic-は] age [than-より] young-[adverb-く] appears-[polite-ます]

年齢より若く見える = 'appears younger than (her) age.' 見える here is 'to appear/look' (not 'to be visible'). より marks the comparison. 若く is the adverbial form of 若い.