The boxart for this game reminds me of Mario Party 2's, except instead of having all the characters dressed in costumes and showing the boards resting on clouds, they seem to have the characters now performing actions and have a bunch of floating island below, which can be assumed to be the design of the boards.
Another note which helps show that is that the first island on the left looks like that one building that appears in the first board from that video shown from when the game was first announced.
Believing that these show the central themes of the board, what else do the other islands show? Probably, like what
Brookelas said, could be some sort of music room. Better guess than anything I could ever think of - but what would be the central gimmick?
And then there's another one to the right, which looks to feature some kind of tree. Going with the others as reference, it probably will be the main feature of it's board. Probably something regarding platforming or something since there happen to be floating ground pieces alongside the island.
Now I'd actually would like to take a look at
what it is the characters are doing on it. As we can obviously see right away,
Mario's riding that rocket with a dice block presumable labeled 0-5 like that one that was shown in the video, which might mean that what the characters are doing
might actually be showing the board gimmicks of individual boards.
This also can be shown by
Waluigi in the top-right corner, who seems to be
holding 2 cards that look identical to those featured in the first they showed (and that's also as many as any character held in total, mind that for later). Of course,
now he's riding a magic carpet as well, so does it seem like we might actually be able to ride those as well in that board?
Now we can see that
Luigi is holding
5 cards as well in his hand - but if you take a good look - the back-side of the cards
have the ShyGuy's mask on it. Could this mean that one of the boards would be hosted by ShyGuys? And what would they do in their own board if they don't do the same thing as in the first board? I have a hunch that we might be playing with cards only similar to how Wii Party had for one of their games (which I forgot what it's called).
Onto
Peach, we can tell that she's riding a bubble for some reason. Could this possibly mean that there will be a course with a gimmick that revolves around bubbles? Of course, bubbles can be seen over most the the top area of the box, so it could also count as a menu-type thing instead where they just have bubbles pass the screen or something like that. Of course, we can see near Wario that a Mushroom is also trapped inside a bubble, so maybe they could have their own board where they have items? Seeing Boo with that Mushroom and Bowser Jr. with that Green Koopa Shell could say that you have to collect the items in the bubbles and use them against others or something.
Finally, just looking at the characters on the boxart, we can see all the main Mario Party players all ready to party -
Mario, Peach, Wario, Toad, Luigi, and Peach were all the confirmed players we already know, with
Waluigi, Yoshi, Rosalina, Boo, Bowser Jr., and a few common enemies (most likely not going to be playable due to their structor/numbers) also appear. I think it's safe to say that
Yoshi and Waluigi are also going to be playable with them, and
Rosalina won't be as she waits for you at the end of the Space board, leaving only
Boo and Bowser Jr. left undetermined.
Also - with the fact that they both seem to be holding items - could it be possible that both of them are joining the roaster as well?
If memory serves, most (if not all) Mario Party box-arts featured all playable characters as well as a few NPCs.
We've already got the few NPCs, but what about these two? If so, Boo will be making a re-appearance as a playable character, and Bowser Jr. will make a first MP as a playable character, just like how he was intended to be originally in Mario Party 9 (or at least a CPU story player only).
And that's all that the box really shows. Sure, there happen to be a few spaces around, but those are just red, blue, and green spaces, and we already know what they might represent.
...and yes, there is a Bowser space, but all that shows is that Bowser's returned to stur up trouble. How this could relate to Bowser Jr. being playable (since Bowser is normally nice to his
favorite son).
...oh yes, and apparently, there's
MINI-STARS as well on here~ What could that mean, hrmm...?
...there's my rant about the Box.

I hope you enjoyed it. ;D
...it's an interesting box art, btw.