I just happened to see it somewhere & was curious what it means. Google translate says "let Justice be done, though the world perish" or "Let justice and the world perish.". I have the Google translate extension which lets you highlight something & translate it, which gives me the first translation. When I go to the site, & type it in, I get the second one, with a checkmark saying it's verified. Which is it? I thought maybe it was the first one because from what I remember, "et" is "and", & mundus is similar to "mundo" (Spanish & Esperanto).
There are two verbs here, both in the subjunctive; on its own, without further context, that generally indicates a desire or wish ("let…").
So I would translate this as let there be justice, and let the world perish. The meaning of the first part is literally "let justice be made" or "let justice be done", but this is the same verb we see in the Vulgate version of Genesis: fiat lux, "let there be light".
Let justice be done though the world perish.
That (excellent) translation uses the rare English present subjunctive on "perish". Here's a more prosaic though less elegant translation:
Let the law be followed even if the world perishes.
Immanuel Kant explains the meaning of the sentence in Project for a Perpetual Peace (1795). It's a legal maxim meaning that cases should be judged according to the law without regard for political consequences. If the true, just conclusion of a case would anger powerful people in high office or trigger mass public protests or cause material suffering, then pronounce the true, just conclusion anyway. The reason is that without justice and law there is no civic order, so bending a decision to accommodate such pressures actually damages the civic benefits that were the basis of those pressures.
A more common expression of the maxim is Fiat justitia ruat caelum, "Let justice be done though the heavens fall."
One of the most famous invocations of the maxim, which illustrates its meaning especially well, occurred in England in 1768 at a court proceeding to reverse a sentence of outlawry* that Parliament had pronounced upon the political activist John Wilkes. Much public furor surrounded the case. A violent mob had attacked the building and tried to free Wilkes by force. Some in the press demanded that the rioters be appeased with the legal decision they wanted lest an insurrection ensue. Amidst this chaos, while presenting the legal basis of his ruling, the judge, Chief Justice Lord Mansfield, spoke these words [Rex v. Wilkes (1769), pp. 346–7]:
But here, let me pause!—
It is fit to take some notice of the various terrors hung out; the numerous crowds which have attended and now attend in and about the hall, out of all reach of hearing what passes in Court; and the tumults which, in other places, have shamefully insulted all order and government. Audacious addresses in print dictate to us, from those they call the people, the judgment to be given now, and afterwards upon the conviction. Reasons of policy are urged, from danger to the kingdom, by commotions and general confusion.
Give me leave to take the opportunity of this great and respectable audience, to let the whole world know, all such attempts are vain. Unless we have been able to find an error which will bear us out, to reverse the outlawry, it must be affirmed. The constitution does not allow reasons of State to influence our judgments: God forbid it should! We must not regard political consequences; how formidable soever they might be: if rebellion was the certain consequence, we are bound to say “fiat justitia, ruat caelum.”
*Outlawry is deprivation of the rights and protections normally accorded to citizens; hence "outside the law".