Not too long ago, I wrote about the Securities and Exchange Commission's confusing classification of subsidiaries.  See The Case Of The Wholly Owned, But Not Totally Held, Subsidiary That May Or May Not Be 100% Owned.  Since this blog is concerned primarily with California corporate and securities laws, I would be remiss in not adding a mention of the meaning of "subsidiary" under the General Corporation Law:

“subsidiary” of a specified corporation means a corporation shares of which possessing more than 50 percent of the voting power are owned directly or indirectly through one or more subsidiaries by the specified corporation.

Cal. Corp. Code § 189(a).  However, for purposes of Section 703, which denies voting power to shares of a corporation owned by its subsidiary, a “subsidiary” of a specified corporation means a corporation shares of which possessing more than 25% of the voting power are owned directly or indirectly through one or more subsidiaries as above by the specified corporation.  Cal. Corp. Code § 189(b).

Etymologically, the word "subsidiary" is derived from the Latin verb "sedere", meaning to sit, and the Latin prefix "sub", meaning beneath or under.  Thus a subsidiary literally is something that sits below something else.