The ancient Romans knew how to keep the interior of their villas dry when it rained. They covered their roofs with overlapping curved tiles so the "imber" (Latin for pelting rain or "rain shower") couldn't seep in. The tiles were, in effect, "rain tiles," so the Romans called them "imbrices" (singular "imbrex"). The verb for installing the tiles was "imbricare," and English speakers used its past participle - "imbricatus" - to create "imbricate," which was first used as adjective meaning "overlapping (like roof tiles)" and later became a verb meaning "to overlap."
Late Latin imbricatus, past participle of imbricare to cover with pantiles, from Latin imbric-, imbrex pantile, from imbr-, imber rain; akin to Greek ombros rain