What is Story Now? Maybe add a basic definition in the OP for those who have no idea what it means. Might turn out I'm doing it intuitively. ;-)
Others have taken a crack at this, but here's how I put it: Story Now rose from the idea of Story Before. If you imagine a dungeon, that's story before -- the nature, paths, obstacles, events of that dungeon exist before play. This is obviously a great way to play, because it's the most common way to play and people love it (I'm one of those people). Story Now, though, is about making all of that work at the table, in the moment, and not prepping it before hand. This isn't the same as "winging it," which it's often confused with, because even with "winging it" the GM is the one driving the story. Instead, in Story Now, the story is driven by play -- the GM usually tightly constrained as to what they're allowed to introduce and when.
Largely, Story Now, for me, is driven (mostly) by the following:
1) Be a Fan of the PCs
2) Play to find out what happens
3) No Force
1) Be a Fan of the PCs. This seems like it's obvious, but there's a really key things here -- we enjoy watching the things we're fans of overcome. I'm a 007 fan, for instance, but I don't want to watch 007 enjoy a relaxing vacation (if that's possible). I want to see 007 get beat up, put in impossible situations, and then how he comes out of those! Being a Fan of the PCs doesn't mean go soft, or be nice, it means that you, as GM, really want to see how these PCs deal with the firehose of adversity you're going to point at them. It means creating situations that try these PCs, that go right for their soft spots, and then loving what happens next. It absolutely means no blocking, though -- you cannot predict what's going to happen and drive for that, instead you have to let the PCs be the PCs.
2) Play to find out what happens. This also seems obvious, but it's, again, not. We're not talking about seeing how the PCs overcome these trolls the GM put in the dungeon (or whatever), but instead we're going to play to see if a dungeon even exists, much less trolls. Every action in a Story Now game has the capability to go off in a completely new direction, and usually does. Prep is nearly impossible in these games, because it will be challenged and renders useless very quickly. You must hold onto prep very lightly, as it's likely to go out the window very quickly.
3) No Force. This is critical in Story Now games -- the GM cannot push any outcome or result at all, ever. This goes with 2) above in that the GM can't use the usual tools of GMing to run a Story Now game. You can't have quantum ogres, and you can't have detailed prep down to the cobblestones of a town. These force outcomes. The only thing that's constricting in a Story Now game is what's already in play -- ie, what's been shared at the table, for everyone. Everything else is a possibility.
Now, these things do not work very well with a lot of mainstream games, D&D being one of them. This is because the mechanics of these games do not reinforce this mode of play, and sometimes actively fight against them. D&D's core concept of "the GM decides" is a challenge to Story Now play. Other games build these concepts into the very fabric of the system, and so the system reinforces play in a way that's utterly absent in a game of D&D -- to do Story Now in D&D the GM is going to need to push it hard, and that's kinda not in-line with the concept. You can do it, but it would take a big hack of the system or just outright ignoring it, and if you're ignoring the system, you're going to lose a lot of the ways that system aids Story Now play. Specifically, systems tuned for Story Now have robust mechanics that create complication as they work. This aids in driving play in unexpected ways, and creating a solid, consistent play that isn't at all what most people consider "winging it" to look like. Story Now games work very well, but are a hard shift in perspective from traditional D&D style, GM centered games.