early 14c., "an opening in a wall or hedge; a break, a breach," mid-13c. in place names, from Old Norse gap "chasm, empty space," related to gapa "to gape, open the mouth wide," common Proto-Germanic (cognates: Middle Dutch, Dutch gapen, German gaffen "to gape, stare," Swedish gapa, Danish gabe), from PIE root *ghieh- "to yawn, gape, be wide open."
From late 14c. as "a break or opening between mountains;" broader sense "unfilled space or interval, any hiatus or interruption" is from c. 1600. In U.S., common in place names in reference to a deep break or pass in a long mountain chain (especially one that water flows through), a feature in the middle Appalachians.
1540s, "state or quality of being ample," from French amplitude or directly from Latin amplitudinem (nominative amplitudo) "wide extent, width," from amplus "large, spacious" (see ample). Amplitude modulation in reference to radio wave broadcast (as opposed to frequency modulation) first attested 1921, usually abbreviated A.M. Related: Amplitudinous.
1610s, "suitcase, soldier's kit bag," from French valise (16c.), from Italian valigia, a word of uncertain origin. Attested in Medieval Latin forms valisia (early 15c.), valixia (late 13c.). "The name is generally given to a leather case of moderate size, opening wide on a hinge or like a portfolio ...." [Century Dictionary]
1560s, "break or opening" in a material object, especially in anatomy, from Latin hiatus "opening, aperture, rupture, gap," from past participle stem of hiare "to gape, stand open," from PIE root *ghieh- "to yawn, gape, be wide open." Sense of "gap or interruption in events, etc.;" "space from which something requisite to completeness is absent" [Century Dictionary] is recorded from 1610s.
"amorous or designing widow," 1907, from the English title of Franz Lehar's operetta "Die Lustige Witwe" (1905). "The Lusty Widow" would have been more etymological (see lust (n.)), but would have given the wrong impression in English. Meaning "a type of wide-brimmed hat" (popularized in the play) is attested from 1908.
1520s, "chatter, frivolous talk;" see chat (v.). Meaning "familiar conversation" is from 1570s. As a name for birds with chattering cries, 1690s. Chat show for what in U.S. is a talk show is attested from 1967. Chat room in the online sense is attested by 1994, from the days when AOL ruled the World Wide Web.