She often goes shopping on her days off.

Literal

She [topic-は] holiday [whenever-になると] often shopping [for-に] goes.

~になると is a compact 'whenever it becomes X / when X comes around,' built from になる ('become') + the conditional/sequential と. The と here is the recurring/habitual と: it pairs with predicates of regular consequence to mean 'every time X, Y happens.' 買い物に行く demonstrates 'purpose に' — the masu-stem of a verb (買い→ buying, here just the noun 買い物 'shopping') plus に plus a motion verb expresses going *for the purpose of* doing X. Same pattern: 食事に行く ('go to eat'), 散歩に行く ('go for a walk'). The polite ます form gives the whole sentence a calm, neutral register.