After using iOS 7 for the past 2 days, the best word I can use to describe it is alive.
The layers -- background, springboard, translucent overlay -- have a very fluid, and quick feel to them. The whole OS feels very lightfooted and lightweight. It has almost a "fun" feel to it. Apps open instantly. Boot time is under 12 seconds as opposed to 45-60 sec. When locking the phone it fades to black and when shutting down the phone the screen shuts from top to bottom. Most of this is a very ethereal experience that is so fine as to render it just below the level of consciousness that unless you lose yourself in the experience of just feeling what's happening, you may miss altogether. This is one of the reasons you need to actually use it to comprehend it.
Note that the home screen is treated like an app in the OS like any other app. Switching between apps via Control Center causes the apps to slide right, above the background. The background image is treated as the inner view of the hardware, and apps/animations/actions are performed above the backdrop of the wallpaper. When multitasking, the homescreen is displayed as yet another app that can be opened. It's just the front living room to the rest of the house. The end result of all the elements of design is to make me feel like the phone is always there and on and a part of the physical universe, and the apps I use as the software overlay augmenting my experience. Apps are visible when I need them and invisible when they're not in use.
This is a high level overview of the OS itself, and not of the experience using the individual apps; but it's the first part of getting to understand the thinking and design language that lies in iOS 7.
I'd love to hear other users' thoughts about the visceral experience of using the OS, and welcome any questions others may have. We're still only at the beginning this experience, and other understandings and viewpoints will inevitably surface over prolonged use.