From Latin 'civicus' (of citizens), from PIE *key- (to settle) — the same root that produced Germanic 'home.'
Relating to a city or town, especially its administration; relating to the duties or activities of citizens.
From Latin 'civicus' (of or relating to a citizen), an adjective derived from 'civis' (citizen, a member of a city-community), from PIE *k̑ey- or *k̑ei- (to lie down, to settle, to be at rest in a place). The PIE root *k̑ei- generated the whole cluster of settlement-words: Greek 'koiman' (to put to sleep, to settle), Sanskrit 'śete' (lies down), and crucially the Latin civic family — 'civis' (one who settles in a place → citizen), 'civitas' (city-state, the settled community → English 'city'), 'civilis' (civil) and 'civilitas' (civilised conduct → 'civility'). A citizen is therefore at root 'one who has settled' — someone who has a place, and whose identity is bound to that settlement. The English adjective 'civic' arrived in the mid-16th century
The English word 'home' and the Latin word 'cīvis' (citizen) both descend from PIE *ḱey- (to settle, to lie down). Through Germanic, the root became Old English 'hām' (home, estate); through Latin, it became 'cīvis' (one who has settled in a community). So 'civic duty' and 'going home' are built from the same ancient concept: the place where you have