late 14c., from Old French edifice "building" (12c.), from Latin aedificium "building," from aedificare "to erect a building," from aedis, variant of aedes "temple, sanctuary," usually a single edifice without partitions, also, in the plural, "dwelling house, building," originally "a place with a hearth" + combining form of facere "to make, to do" (from PIE root *dhe- "to set, put").
Aedis is from PIE *eidh- "to burn, burning" (source also of Sanskrit inddhe "burst into flames;" Avestan aesma- "firewood;" Greek aithein "to burn," aithos "fire;" Latin aestas "summer," aestus "heat;" Lithuanian iesmė "firewood;" Old Irish aed "fire," Welsh aidd "heat, zeal;" Old English ād, Old High German eit "funeral pile," Old Norse eisa "burning coals"), which is perhaps related to the root *as- "to burn, glow."