At just about every E3 and TGS I can remember, Sony has held some pretty excellent "breakout" sessions where developers get to sit down in a quiet conference room and give in-depth, hour-long demos far away from the deafening roar and superficial hands-on sessions of the show floor. I came out of today's Infamous breakout with a page full of notes, so let me see if I can break down the salient takeaways for you.

The animated comic panels and voiceover of the intro conveyed a dense amount of story information in a short time, not just about the broader storyline, but with a personal touch as well. I picked up through quick context some of the supporting characters, like your conspiracy-theorist sidekick Zeke and a girl named Trish, who I took to be the game's love interest. The point is, this ripped-from-a-comic-book intro sequence looked super snazzy and got me interested in the premise from the get-go.
Cole's Abilities. So the dude is a superhero of the electrical variety. First, that gives you a basic lightning-zap ability that you can aim at anyone to give them a quick (sometimes lethal) jolt. The lightning propagates from surface to surface, so you can jolt more than one enemy (or bystander) at a time. Naturally, metal structures are especially conductive; the demo showed a mostly metal power station where you could basically go buck wild, shooting lightning every which way and having it travel along the structure's steel framework to make a lot of havoc for the enemies occupying the place. The electrical abilities will be multipurpose: you'll also be able to electrify water, for instance, or kickstart dead machinery by providing current.
Sony introduced a new ability in this demo called post-cognition. This will let you meld minds with the recently deceased to find out what sordid circumstances led up to their deaths. In gameplay terms, post-cog seems like a jumping-off point for some missions--in the example given, a dead woman's missing husband provided the impetus for an objective that needed to be completed. This power is obviously not electricity-related, so I'm curious where else Cole's arsenal will go as the game progresses.
Getting Around Town. Cole's a pretty acrobatic guy; he can climb up building fronts and lamp posts with ease in the early part of the game. I saw overt shades of Assassin's Creed's urban climbing mechanics in the demo, set early on in the game. It looked easy to get from point A to point B, even if A was at street level and B was on top of a five-story apartment building. You'll be able to trash the environment to make new paths in some cases, like when Cole zapped an antenna on top of an adjacent building and knocked it down to act as a bridge.

Good Versus Evil. So there's a basic morality component here, which tracks your every move and swings a good/evil pendulum accordingly. Citizens love you if you're a good guy; they'll flee in terror at your approach if you're the villainous sort.
Here's a quandary: Cole needs to absorb electrical current to use his powers. In most situations you can pull it right out of the air, but what about areas of Empire City where the power's out? You can also pin down bystanders and go all electro-vampire on them, pulling energy right out of their bodies. But is that really the right thing to do? You're a resourceful superhero, you can think of a friendlier way.
Conversely, you've also got a healing power that will bring people back from the brink of death, and you'll have combat abilities that will let you subdue the baddies in a non-lethal manner. But when you've got powers this explosive, who wants to be a goody two-shoes all the time? Oh, the moral ambiguities of the superhuman.
I'm impressed with what little Sony's revealed of Infamous so far. The game is still seven months away from release, so while things like a consistently compelling storyline and satisfying character progression remain to be seen, the basic framework--a decaying urban playground and larger-than-life physics-based powers to use in that city--seems to be in place.
Lastly, have a gander at the new shots of Infamous released at TGS today.