故乡 is a deeply emotional word in Chinese culture. The famous Tang dynasty poem by Li Bai: 举头望明月，低头思故乡 (I raise my head to gaze at the bright moon, and lower it thinking of my hometown).
usage
故乡 is more literary/emotional than 老家 (lǎojiā), which is the colloquial way to say 'hometown.' Both are very common.
culture
"举头望明月，低头思故乡" (I raise my head to gaze at the bright moon, and lower it thinking of home) — from Li Bai's "Quiet Night Thoughts" (静夜思), one of the most memorized Chinese poems.
