The maidens who select the battle-dead and carry half of them to Valhalla.
Documented
Valr plus kjósa
The word assembles from valr, the slain, and kjósa, to choose. Eddic poems place valkyries over battlefields and at Odin's benches, serving mead to the chosen. Linguistically and textually secure.
Assessment: Documented etymology with poetic attestation. The title was literal.
Stories
Wagner dressed them
Winged helmets, breastplates, the Ride: the modern image is nineteenth-century opera costume, finalized in 1876. The medieval texts give no uniform and sometimes make them swan-maidens or mortal princesses.
Assessment: Documented staging history. The Valkyrie you picture is a costume designer's decision.
Interesting claims
A memory of real women who decided
The claim: valkyries preserve a memory of ritual specialists, perhaps priestesses who marked the doomed before battle or presided over sacrificial selection.
Assessment: Argued seriously within Viking-age ritual studies and resisted by textual purists. Evidence is circumstantial: loom-weight burials, seeress graves, and analogy.
Sources and further reading
Cleasby-Vigfusson, valkyrja, the chooser of the slain
Poetic Edda, Völundarkviða and Helgi lays
Wagner's 1876 costume designs, Bayreuth records
Neil Price, The Viking Way, on ritual specialists
Worth asking
Who gets to choose the slain now, and what do we call them?