When you're online, someone starts a challenge, something like "everyone do a jump" or "everyone crash into each other while flying off a bridge."
Read earlier on the Criterion Boards that you don't necessarily need to make a new save to get trophies. For instance, if the trophy is "win a race," you can do that with your existing save, because you can win a race any time. If it is "win 1 race," then you'd need a new file because you only win your first race once. That should make the bike trophies easier for me, as I was already well on my way to 100%.