late 14c., "open letter or official document from some authority granting permission to do something; a licence granting an office, right, title, etc.," shortened from Anglo-French lettre patent (also in Medieval Latin litteræ patentes), literally "open letter" (late 13c.), from Old French patente "open," from Latin patentem (nominative patens) "open, lying open," present participle of patere "lie open, be open" (from PIE root *pete- "to spread").
The Letters Patent were ... written upon open sheets of parchment, with the Great Seal pendent at the bottom ... [while] the 'Litteræ Clausæ,' or Letters Close, ... being of a more private nature, and addressed to one or two individuals only, were closed or folded up and sealed on the outside. [S.R. Scargill-Bird, "A Guide to the Principal Classes of Documents at the Public Record Office," 1891]
Meaning "a licence granted by a government covering a new and useful invention, conferring exclusive right to exploit the invention for a specified term of years" is from 1580s.