"a round, vaulted roof, a hemispherical covering of a building," 1650s, from French dome "a town-house; a dome, a cupola" (16c.), from Provençal doma, from Greek dōma "a house, housetop" (especially in reference to a style of roof from the east), related to domos "house," from PIE root *dem- "house, household."
In the Middle Ages, German dom and Italian duomo were used for "cathedral" (on the notion of "God's house"), so English began to use this word in the sense "cupola," a dome at the intersection of the nave and the transept, or over the sanctuary, being a characteristic architectural feature of Italian cathedrals.
The word was used in U.S. also with reference to round summits of mountains, roofs of railroad cars, etc. The etymological sense "a building, a house," especially a stately one, was borrowed earlier in English (1510s) but mostly was restricted to poetry.