Parenthesis

The general meaning of parenthesis is "An explanatory or qualifying word, clause, or sentence inserted into a passage with which it has not necessarily any grammatical connexion, and from which it is usually marked off by round or square brackets, dashes, or commas" (OED). In some special areas, such as Logic, it has other meanings. In American usage, it is the noun used to name what we British call [round] brackets.

The general meaning is of something inserted in a sentence, or other unit of grammatical structure, which is not essential; but which gives some additional matter. This added matter is something that the writer (or speaker; in this sense, parenthesis is not limited to writing) feels is of interest, but that the reader may ignore.

You may want to see an article on the two forms parenthesis and parentheses.