Running the gauntlet is a phrase meaning "to endure hardship or criticism from many sources at once" or "to endure a prolonged test". Often, to run the gauntlet implies a sort of hazing or initiation: "He had to run the gauntlet like all the other newbies, but he's matured into a solid member around here."
This phrase comes from a military punishment of bygone days. Those soldiers or sailors who disobeyed orders or committed other minor infractions would be stripped to the waist and made to run between two ranks of men, all armed with cudgels, switches or knotted cords. This ordeal was no doubt as harrowing as it sounds. Originally, the term was to run the gatloppe (many variant spellings exist: gantloppe, gantlop, gatlop and so forth). Gatlopp is a Swedish term meaning "a running course" or "street race" (the first part of the word is related to our English gait and also gate in the British sense of a concourse or path).
The English-speakers took this phrase and ran (or loped) with it. Slowly, the unfamiliar term gatloppe became gantlope, then the more familiar spelling of gauntlet (some writers prefer the spelling gantlet). The first use of this phrase being used figuratively was in Oliver Goldsmith's She Stoops To Conquer (1773). By the early 19th Century, the phrase had been standardized in English to its familiar form.
The word gauntlet, in this context, has nothing to do with the armored gloves of that name. The name of the glove comes from a Teutonic word wantus which came to English by way of French (as so many do), gant, simply meaning glove. Some sources have claimed that the gloves were used to batter people on the running course, but this appears to be apocryphal.
Thanks to soriyya for fixing up my Swedish, a language I have next-to-no foundation in !
Mordock, John and Korach, Myron "Common Phrases and Where they Come From" (the Lyons Press, Guilford, CT, 2001).
Rees, Nigel, "the Cassell Dictionary of Word and Phrase Origins" (Cassell, London, 1996).
the Maven's Word of the Day: http://www.randomhouse.com/wotd/index.pperl?date=19990621
World Wide Words: http://www.worldwidewords.org/weirdwords/ww-gan1.htm
Special tip of the old chapeau to Mr. Webster 1913 for help with the etymology of specific words.