What does Popilius mean when he says, "I wish your enterprise today will thrive" in Julius Caesar, act 3, scene 1?

The effect of Popilius' words is to add further to the dramatic tension leading up to the assassination. Popilius means exactly what he says. He knows that Cassius and a number of other conspirators are going to try to kill Julius Caesar and he is wishing him good luck. Why would Popilius want to wish Cassius good luck or to say anything at all? Popilius is playing it safe. He wants to be recognized as a supporter of the conspirators because he assumes there will be a lot of "collateral" bloodshed after the event, and he doesn't want to be one of the people he expects to be eliminated as a sympathizer of Caesar. On the other hand, if the enterprise doesn't "thrive," then Popilius would prefer not to be known as one of its supporters. That is why he only speaks in guarded terms to one person, to Cassius. But he obviously knows a lot, including the fact that Cassius is the instigator of the assassination plot.

Cassius has been recruiting people to take part in assassinating Caesar since before the play even began. It was inevitable that word should get around that there was such a conspiracy brewing and that Cassius was behind it. Some of the people Cassius approached who declined to get involved would still know about it and might very well mention it to others. So there could be a number of people in the crowd who expect an assassination attempt to occur, but Popilius is smart enough to work both sides of the street, so to speak. He is looking ahead. He wants to be on the side of whoever ends up holding the power in Rome. Right after Popilius talks to Cassius and alarms him, Brutus observes:

Cassius, be constant.
Popilius Lena speaks not of our purposes;
For, look, he smiles, and Caesar doth not change.

So Popilius goes to Cassius to hint broadly that he is a sympathizer, and then he goes directly to Julius Caesar, probably to assure him of his good will and to say that he hopes Caesar's "enterprise will thrive," i.e., he hopes Caesar will be crowned king that morning. 

It is probably worth noting that when Antony, Octavius, and Lepidus have seized power and are choosing the men they will exterminate because of their sympathies with the assassins, the name of Popilius Lena does not come up. He may have been able to save himself by his foresight. 

What does Popilius mean by "I wish your enterprise today may thrive" in Act 3, Scene 1 of Julius Caesar?

In Shakespeare's Julius Caesar, in Act III, scene i, Popilius says to Cassius that he hopes his "enterprise" or his ambitions will thrive. Cassius is paranoid because of the plans he and co-conspirators have to assassinate Caesar. It may at first seem that Popilius is privy to their secret plans. This also provides the audience with a breathless moment, wondering if the plot is to be denounced and stopped. However, Popilius is not speaking of treachery. It seems he is simply wishing Cassius success in his business that day—whatever it is; as innocent as our parting words, "Have a nice day."

If we search through the scene, we will note that there is a great deal going on! The soothsayer is repeating (to Caesar's annoyance) his "it's-getting-old" warning regarding "the Ides of March." Artemidorus is pushing Caesar to read his letter, which does carry a warning.

There is irony here in several ways. The two men who might save Caesar are the two men he dismisses. It is also noted that it is ironic that Caesar sends Artemidorus away, noting that Caesar will deal with any personal affairs last. Seemingly a noble gesture, he goes on to show he is not at all noble, but really quite full of himself.

Caesar believes that he is a god, not a mere mortal. He also sees himself as the heart and soul of Rome. Consider his response as Metellus Cimber humbles himself before Caesar, asking that he reconsider the emperor's banishment of Cimber's brother.

CAESAR:
I must prevent thee, Cimber.
These couchings and these lowly courtesies
Might fire the blood of ordinary men
And turn preordinance and first decree
Into the law of children. Be not fond
To think that Caesar bears such rebel blood
That will be thaw'd from the true quality
With that which melteth fools, I mean sweet words,
Low-crooked court'sies, and base spaniel-fawning. (40-48)

Caesar responds that this kind of humble behavior from Metellus might work on "ordinary men," and might lead them change the laws to those dealing with children. However, it will not sway Caesar's purpose as it would the purpose of fools (which Caesar believes he is not)—showing irony once again in that Caesar is a fool by virtue of his inflated ego—and his failure to recognize that his "friends" are really enemies.

He also says:

Know, Caesar doth not wrong, nor without cause
Will he be satisfied. (52-53)

Caesar says he's never wrong! And again he alienates those around him by comparing himself to the Northern Star, a heavenly body that directs travelers and sailors at night—guiding each to safety...nearly impossible to survive without. He notes that like the star fixed in the heavens, he cannot be moved:

But I am constant as the northern star,
Of whose true-fix'd and resting quality
There is no fellow in the firmament. (66-68)

In this bedlam—as many people seek the attention of Caesar, as well as perhaps an almost palpable feeling of tension from the conspirators—it is easy to imagine that Popilius (who is opposed to Caesar) speaks with knowledge of Cassius' intent; but he never shows this. We can assume that he is simply a part of the melee, delivering solicitous greeting to Cassius as he might any other man present—perhaps vaguely aware of Cassius' discontent—but not suspecting any action based on his unhappiness.

Amid the confusion and rising suspense of the plot development, it is simply Cassius' unique situation which causes him (and the audience) to pause and wonder at Popilius' comment.

In William Shakespeare's Julius Caesar, Act III Scene 1, Popilius Lena says to Cassius: "I wish your enterprise today may thrive". When Cassius nervously enquires what enterprise is meant, Popilius merely says 'Farewell' and departs. At first, Cassius interprets this to mean that their plot to assassinate Julius Caesar has been discovered, but Caesar's demeanour does not change after Popilius speaks with him and Brutus suggests that this means Popilius has not discovered the plot. Contextually, it appears that Popilius assumed that Cassius, as many others, was approaching Caesar with a petition or request and was simply being polite and wishing him good luck.