MORPHEUS: I imagine that right now you're feeling a bit like Alice, tumbling down the rabbit hole.
Neo can't help but agree.
Let's put ourselves in Neo's shoes for a moment (ah, they've got quite a shine to them). Our computer has been hacked, our mouth has been sealed shut with our own skin, we've been bugged, then it was all a dream, then we were debugged (so it wasn't a dream?) and now we're meeting this deity-like figure named Morpheus who we've only hear rumors about.
It sounds a bit too strange to be real (well it's not technically real, but that's beside the point). But Morpheus isn't done yet. When offering Neo a choice of pills, he again alludes to Alice, saying:
MORPHEUS: take the red pill, you stay in Wonderland. And I show you how deep the rabbit hole goes.
Alice's Adventures in Wonderland, Lewis Carol's most well known book, is about a girl who travels to a…very strange place. There's really no other way to say it, you'll have to read it for yourself because it's quite the trip.
Morpheus is comparing Neo's experience to the experience of Alice because of all the unbelievable things that are happening to him. Earlier Trinity tells Neo to "follow the white rabbit." He ends up spotting a snazzy white rabbit tattoo on the shoulder of a partygoer named Dujour, and, heeding Trinity's spooky instant message, he follows her.
In Alice in Wonderland, Alice finds Wonderland by following the a cute little white bunny (who is running through the "real world" wearing a waistcoat with a watch and worrying about his tardiness. You know, just your typical rabbit) who leads her to the rabbit hole where the adventure begins.
So the white rabbit is more than Dujour's tattoo, it's a metaphor for following one's curiosity to an impossible land. What makes this metaphor especially interesting is that Neo is, in a way, already in Wonderland. He is actually about to emerge from the rabbit hole… and boy is he in for a surprise.
Well, on the bright side, at least he doesn't have to eat from a magical mushroom to change his size—that would have been quite another movie.