"To throw down the gauntlet" is to issue an open challenge; "to pick up the gauntlet" is to accept that challenge. The word gauntlet was borrowed from French in the 15th century. Its literal meaning in French is "little glove," and it originally referred to a protective glove worn with medieval armor. The phrases arose from the medieval custom of throwing down a glove to issue a challenge to a rival combatant and picking up the glove to accept the challenge. These phrases (with many variations) persist in figurative use, and gauntlet also now refers to several varieties of gloves, both protective and fashionable.

By the way, some controversy surrounds the spelling of the variant forms gauntlet and gantlet. The argument is sometimes heard that gantlet is the only correct choice in the phrase "to run the ga(u)ntlet"; however, this use of gauntlet has a more complex history. To run the ga(u)ntlet was originally a form of military punishment in which a prisoner was made to pass between two rows of men armed with clubs or other weapons. The original name for this punishment was gantlope. Gantlet was simply one of several spelling variations, as was gauntlet.

We do not know exactly how gantlet came to be regarded as the preferred spelling in "to run the ga(u)ntlet." The distinction gantlet (punishment)/ gauntlet (glove) seems to have arisen in the United States in the 19th century. British dictionaries have never recognized the distinction, and gantlet is no longer a spelling variant in British English.