Etymology
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executive (adj.)

1640s, "capable of performance" (a sense now obsolete), also "of the branch of government that carries out the laws," from Latin executivus, from past participle stem of exequi "follow after; carry out, accomplish" (see execution). The sense of "concerned with or pertaining to the function of carrying into practical effect" is from 1670s. The noun meaning "person or persons invested with supreme executive power in a country" is from 1776, as a branch of government charged with the execution and enforcement of the laws. Meaning "high-ranking businessman, person holding an executive position in a business organization" is by 1902 in American English; hence the adjectival sense "stylish, luxurious, costly" (1970s). Executive privilege in reference to the U.S. president is attested by 1805, American English.

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department (n.)

c. 1500, "a ceasing, an ending; a going away, act of leaving" (obsolete in this sense), from Old French departement "division, sharing out; divorce, parting" (12c.), from Late Latin departire "to divide" (transitive), from de- "from" (see de-) + partire "to part, divide," from pars (genitive partis) "a part, piece, a share, a division" (from PIE root *pere- (2) "to grant, allot").

French department came also to mean "group of people" (as well as "departure"), and from this by 1735 English had borrowed the sense of "separate division of a complex whole, separate business assigned to someone in a larger organization, distinct branch or group of activities" (science, business, manufacture, the military). The specific meaning "separate division of a government" is from 1769. As an administrative district in France, from 1792.

Department store "store that sells a variety of items, organized by department" is from 1878.

The "Department Store" is the outgrowth of the cheap counter business originated by Butler Brothers in Boston about ten years ago. The little "Five Cent Counter" then became a cornerstone from which the largest of all the world's branches of merchandising was to be reared. It was the "Cheap Counter" which proved to the progressive merchant his ability to sell all lines of wares under one roof. It was the Five Cent Counter "epidemic" of '77 and '78 which rushed like a mighty whirlwind from the Atlantic to the Pacific and all along its path transformed old time one line storekeepers into the wide-awake merchant princes of the present day. It was this same epidemic which made possible the world famed Department Stores of Houghton, of Boston; Macy, of New York; Wanamaker, of Philadelphia; and Lehman, of Chicago. [American Storekeeper, 1885] 
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administration (n.)

mid-14c., "act of giving or dispensing;" late 14c., "management (of a business, property, etc.), act of administering," from Latin administrationem (nominative administratio) "aid, help, cooperation; direction, management," noun of action from past-participle stem of administrare "to help, assist; manage, control, guide, superintend; rule, direct," from ad "to" (see ad-) + ministrare "to serve, attend, wait upon," from minister "inferior, servant, priest's assistant" (see minister (n.)).

Early 15c. as "management of a deceased person's estate under a commission from authority." Meaning "management of public affairs" is from 1680s; hence, "executive power in a government" (1731), though later in Britain government was used in this sense. Meaning "a U.S. president's period in office" is first recorded 1796 in writings of George Washington.

The administration of government, in its largest sense, comprehends all the operations of the body politic, whether legislative, executive, or judiciary; but in its most usual, and perhaps in its most precise, signification, it is limited to executive details, and falls peculiarly within the province of the executive department. ["The Federalist," No. 72 (Hamilton)]
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CEO (n.)
by 1984; abbreviation of chief executive officer.
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dept. 
abbreviation of department, attested from 1869.
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admiralty (n.)
"naval branch of the English executive," early 15c., admiralte, from Old French amiralte, from amirail (see admiral).
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departmental (adj.)

1791, "pertaining to a (French) department, pertaining to a division of a country," from French départmental, from département (see department). Meaning "of departmental systems generally" from 1832. Related: Departmentally.

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MI5 
1939, from abbreviation of Military Intelligence, followed by the department number.
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obstetrics (n.)

"science of midwifery, the department of medicine which deals with the treatment and care of women during pregnancy and childbirth," 1819, from obstetric (adj.); also see -ics.

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civil service (n.)

"the executive branch of the public service," as distinguished from the military, naval, legislative, or judicial, 1765, originally in reference to non-military staff of the East India Company, from civil in the sense "not military." Civil servant is from 1792.

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