1540s, "words, clauses, etc. inserted into a sentence," from Middle French parenthèse (15c.), from Late Latin parenthesis "addition of a letter to a syllable in a word," from Greek parenthesis , literally "a putting in beside," from parentithenai "put in beside," from para- "beside" (see para- (1)) + en- "in" + tithenai "put, place," from PIE root *dhe- "to put, to do" (see factitious ). Sense extension by 1715 from the inserted words to the curved brackets that indicate the words inserted. A wooden parenthesis; the pillory. An iron parenthesis; a prison. ["Dictionary of Buckish Slang, University Wit and Pickpocket Eloquence," London, 1811]
A parenthesis is one of the marks usually called (ordinary, or curved) brackets in the UK or material set off by a pair of brackets (or commas or dashes). I've just used four parentheses to enclose two parentheses – but I wouldn't usually mix senses like this as it gets too confusing. Actually, since one bracket is rarely found without its 'other half', the singular form parenthesis more often refers to the inserted material, but this is not mandatory. To really disambiguate, the term 'parenthetical', used as a noun, is often used for the 'inserted material' sense.