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!)
'There's something fishy going on here.'
'Well,' said Q, jerking her head toward the door to the stairwell, through which the tattooed woman was disappearing. 'You'd better follow the white rabbit, then.'