Meaning

adjective having an illustrious reputation; respected

adjective exerting influence by reason of high status or prestige

originAttested since the 1540s; Latin praestigiosus (“full of tricks”), praestigiae (“juggler's tricks”), possibly an alteration of praestringō (“to blindfold, to dazzle”), from prae- (“before”) with stringō (“to bind or tie”); equivalent to prestige + -ious. Unstressed /ɛ/ is retained by analogy with prestige.

Etymology from Wiktionary, CC BY-SA 3.0