They are far more than the winged warrior-maidens of the opera: the valkyries decide who falls in battle – and who is taken up into Odin’s hall after death. They are messengers of death and honour guard at once, beautiful and terrible.
Valkyries (Old Norse valkyrja, „chooser of the slain") are Odin’s serving battle-maidens. They ride over the battlefields, decide the outcome of the fight and escort the bravest of the fallen to Valhalla. There they bear the drinking-horn to the einherjar.

Their name says it all: they choose the dead. Whoever dies on the battlefield dies because a valkyrie has chosen him. That makes them one of the most ambivalent figures of the mythology – life-sparing for one, death-bringing for another. In Valhalla, though, they set aside the cruelty and become cup-bearers to the fallen heroes.
“Hrist and Mist / I would have bear the horn to me, / Skeggjold and Skogul; / Hild and Thrud, / Hlokk and Herfjotur, / Gol and Geironul, / Randgrid and Radgrid / and Reginleif — / these bear the einherjar ale.”— Grímnismál 36, translation after Henry Adams Bellows (public domain)
The oldest sources show the valkyries darker than Romanticism wished: in the Darraðarljóð they weave the fate of battle on a loom whose warp is entrails and whose weights are human heads. They are no gentle angels, but instruments of Odin’s relentless gathering for the last war.

The most famous valkyrie is Brynhild (Sigrdrífa): because she let the wrong king win against Odin’s will, he pricked her with the sleep-thorn and condemned her to live as a mortal woman. Her awakening and her runic wisdom for the hero Sigurd are among the loveliest scenes of the Poetic Edda.
Valhalla · Odin · Sigurd · The Norse pantheon.
Grímnismál, Sigrdrífumál, Darraðarljóð (Poetic Edda / skaldic), English public domain: Henry Adams Bellows (1923). Snorri Sturluson, Gylfaginning. Scholarship: Rudolf Simek, Dictionary of Northern Mythology; Neil Price, The Viking Way (2019).