。
She lives in this village.
Literal
She [topic-は] this village [in-に] is-living.
住んでいる is the standard way to express 'live in' (residence) — not the present-progressive 'is in the act of living' that English speakers sometimes assume. 住む is treated as a change-of-state verb (the act of taking up residence is one moment), and ~ている describes the resulting stable state — 'lives in.' Note に marks the place of residence, not で. The polite ~ています shifts the register up. A standard early-vocabulary sentence learners encounter when learning location particles and resultant-state ている.