Refers to a waistcoat-wearing, pocket-watch-wielding white rabbit, hurrying along and muttering, “Oh dear! I shall be late!” in Lewis Carroll’s Alice in Wonderland (1865), whom Alice follows down a rabbit hole into Wonderland.
Awesome rock band Jefferson Airplane’s 1967 song White Rabbit retold the story of Alice’s adventures as though they were a psychedelic drug trip. But whether you take it literally or metaphorically, following the white rabbit means following an unlikely clue, an innocuous, unbelievable (but also, frankly a bit ridiculous) sign, to find oneself in the midst of more or less extraordinary, marvelous, amazing circumstances that challenge one’s fundamental beliefs, expand one’s horizons &/or perception of realities, transform one’s perspective, and change one’s life.
The phrase has become commonplace in popular culture; e.g. in the 1999 film The Matrix, the resistance fighter folks use the trope of following a white rabbit to lead Neo/Mr Anderson/The One out of the matrix. Oddly enough, though, the phrase hasn’t filtered through as a metaphor in non-fantastical contexts to any appreciable degree. Outside of science fiction or fantasy, if a writer refers to the white rabbit, s/he is almost certainly specifically alluding to previous uses, usually to Carroll. (We should change that!)