The story
Literally, “grow and shrink”. Compare wax with the German cognate wachsen (“to grow”). Originally (c. 14th century) used referring to the phases of the Moon. Folk etymology has occasionally mistakenly presumed the phrase to be a reference to candles, under the notion that they are produced by applying wax to a wick and then begin to wane once they are lit.
Etymology from Wiktionary, CC BY-SA 4.0.