She's three years older than me.

Literal

She [topic-は] me [than-より] three-years-of-age elder.

A standard comparison-of-age sentence using より. 三歳 uses the counter 歳 (also written 才) for years of age, the same counter used in 何歳 ('how old') and 二十歳 (はたち, irregularly read as 'hatachi' for 20). 年上 ('older,' literally 'year-above') is the standard term for age seniority, paired with 年下 ('younger, year-below'). When the difference matters as a number, it slots in directly before 年上, with no particle needed — 三歳年上 ('three years older'), 五歳年下 ('five years younger').