Actually, it's not even a box. It's a jar. "Pandora's Jar" just doesn't have the same ring to it.
See, somewhere back in the day, someone mistranslated the story and said that Pandora opens a box to release all the badness in the world. But in the original Greek story, it's supposed to be a jar.
Not really important, though. What matters is that Pandora's Box has become a pretty widely recognized symbol. You might hear somebody say, "Don't talk about that; it's a total Pandora's box." That means that if you bring it up, a whole lot of badness (and no hope?) will come from it. Domino effect, people.
For more on the role of Pandora's box in the story, check out our discussion of Pandora as a character.