c. 1300, porche, "covered entrance; roofed structure, usually open on the front and sides, before an entrance to a building," from Old French porche "porch, vestibule," from Latin porticus "covered gallery, covered walk between columns, arcade, portico, porch," from porta "city gate, gate; door, entrance," from PIE root *per- (2) "to lead, pass over."
The Latin word was borrowed directly into Old English as portic. Especially (late 14c.) "a covered walk or colonnade on the front or side of a building." In U.S., used by 1832 for what the British call a veranda.
mid-13c, "a portico or small room forming a projection, a room or building in the form of a large bay window;" mid-14c., "large recessed window, a bay window," from Old French oriol "hall, vestibule; oriel," and Medieval Latin oriolum "porch, small room, gallery," which are perhaps from Vulgar Latin *auraeolum, a dissimilation of aulaeolum, a diminutive of Latin aulaeum "curtain." "Although much research has been expended upon the history of this word, and especially upon the development of the current use in oriel window, the sense history remains in many points obscure and perplexed" [OED].
It projects from the outer face of the wall, being in plan actually hexagonal, semi-octagonal, or rectangular, etc., and is supported on brackets, corbels, or corbeling. When such a projecting feature rests upon the ground, or directly upon the foundation of the building, it is called a bay-window, or a bow-window. [Century Dictionary]