A person, usually a man, who comes to the aid of another, usually a woman, in a gallant and courteous manner.

The present-day use of this phrase is, of course, figurative and refers back to the notion of gallant knights saving fair maidens in distress. The reality behind that imagery is dubious and no doubt owes much to the work of those Victorian novelists and painters who were captivated by the chivalrous ideal of an imagined court of Camelot. Nevertheless, knights did wear armour, and that worn by royalty and the high nobility was highly polished and did in fact gleam and shine.

The earliest references that I've found to the phrase in print date from the early 19th century. That's in The History of Charles the Great and Orlando, by Thomas Rodd, 1812. The line appears in the romantic poem The Ancient Ballad of Prince Baldwin:

Hark! the martial trumpets sounding.
For the gallant fete prepare;
Many a Knight in shining armour
Shews his dauntless prowess there.

Many of these 19th century citations describe imaginary knights who ride to the rescue of swooning maidens. That's almost, but not quite, the figurative use we have now. Present day 'knights in shining armour' may dress as they please. The earliest uses that I've found that summon up the 'shining armour' image in other contexts come from the USA. It's 'armor' there, of course. For example, this piece from The Kenosha Times, September 1857:

"The ticket nominated is composed of able, earnest, honest men - of men by their reputation for personal worth and integrity protected from assaults as by a shining armor."