1620s, from French clinique (17c.), from Latin clinicus "physician that visits patients in their beds," from Greek klinike (techne) "(practice) at the sickbed," from klinikos "of the bed," from kline "bed, couch, that on which one lies," from suffixed form of PIE root *kli- "lean, slope" (see lean (v.)).
Originally in English "bedridden person;" sense of "hospital" is 1884, from German Klinik in this sense, itself from French clinique, via the notion of "bedside medical education." The modern sense is thus reversed from the classical, when the "clinic" came to the patient. General sense of "conference for group instruction in something" is from 1919.