Actually the box/vagina analogy dates waaay back. It's first used by Freud but in a different way. He explained the box imagery in dreams as a reference to womb. Then it's changed to vagina in slang usage.

I was just wondering if many of the North American viewers got this joke or whether it is one of these typically British slang expressions?
as an Australian we share [or USED to] slang more with Brits than americans and it was other way around when I started to visit america regularly on business 30 years that "bush" rather than "box" was introduced to my vocab [by the joke about hooker with her pants on backwards]
http://www.kindleflippages.com/ablog/

Shakespeare used a lot of humor like this.
and a modern day Shakespeare Kurt Cobain did a great song/video called Heart Shaped Box which equated a heart shaped chocolate box to Cortney Love's "nasty" [or tar-pit trap] and his disgust in himself for being captivated by it to his ultimate death at her hands [blamed on suicide of course - money talks].
if coroner had had any will at all for the truth of his death he only needed to watch the video [below] which is one of my all time favourites [and of 42 million others, though I doubt even 1,000 actually understand the message].
She eyes me like a Pisces when I am weak
I've been locked inside your heart-shaped box for weeks
I've been drawn into your magnet tar-pit trap
I wish I could eat your cancer when you turn black
Hey! Wait!
I've got a new complaint
Forever in debt to your priceless advices
the word play of for/four in line 2 is fantastic.

Shakespeare used a lot of humor like this. Back when I was in high school 50 years ago, this was glossed over, but in college, the professors pointed it out to us. In case our virgin ears had missed it.

William Thacker: I've opened Pandora's Box!
Spike: I knew a girl named Pandora in High school once never did see her box though.
Spike's line is pretty obvious as a sexual pun twist of Thacker's line.

I'm a Canadian teenager, and I never had to have this joke explained to me. I thought it was hilarious I never thought of it being British

Exactly. American audiences knew what the joke was. It definitely was the point of the joke to be the dirty version. Not sure how anyone could have missed what Spike was saying. The guy was dirty throughout the film.

Box and Twat have been used as American slang for decades, way before Sarah Silverman. Granted, they're not very commonly used but anyone over 12 would have gotten the joke in my estimation.

Marjorie, whilst all you are saying is exactly what Pandora's box is in the Greek mytholigcal sense, the actual joke in the movie is exactly the british euphemism - that is what makes it so hilarious. That is EXACTLY the intention of the line in this film - not sure how you could possibly think otherwise??William is talking about what you have stated, but Spike turns it around with his comment. Spike's joke fits right in with his personality - this is what makes it so funny!

Sorry to be a pain but whilst I accept that "box" may indeed be a British euphemism for "vagina" that is not the intention of this line in this film.
The real definition of Pandora's box is not British but stems from ancient Greek mythology and is, broadly speaking, as follows:- Pandora's box is an artefact in Greek mythology, taken from the myth of Pandora's creation around line 60 of Hesiod's Works and Days. The "box" was actually a large jar given to Pandora, which contained all the evils of the world. When Pandora opened the jar, the entire contents of the jar were released, but for one hope. Today, opening Pandora's box means to create evil that cannot be undone.
If you want a more detailed explanation may I suggest you look at http://atschool.eduweb.co.uk/carolrb/greek/pandora.html
Hope this is of interest to some of you at least.
I shouldn't have done that. I shouldn't have done that. No, you were brilliant. (Notting Hill)

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Box is a british euphemism for vagina, it's now quite big in America too after Sarah Silverman's parody of SNL's "dick in a box" sketch with her "box in a box" sketch.
She actually introduces lots of Brit words to US audiences, the first time I ever saw an American say 'twat' was on her show.
With your feet in the air and your head on the ground, try this sig with spinach!

after seeing the movie for the umpteenth time tonight, i actually caught that joke for the first time

Lol We do get such innuendo's. Depends on a person's mind. As for myself there's probably nothing that I couldn't make sound dirty
Your love is like a shadow on me all the time