If you’re a typical designer working in the software world, the majority of products you’ll create will have strictly two dimensional interfaces — length & width only, pixels on the screen. As interfaces have evolved over the years many have gained a very simple kind of "depth": lighting effects, drop shadowing, and modeled surfaces. But they are (ironically) strictly surface effects: aids to perceiving flat objects on a flat screen in discreet layers. The illusion of depth is useful for managing a limited amount of space, and contributes to a more detailed and "real"-feeling experience. Yet like piled sheets of paper, they have depth but are not in any meaningful way three dimensional objects.
An alternate dimension that can be added to our otherwise flat interfaces is time.A useful way to frame almost any design problem is through the act of storytelling. A mobile phone design includes the story of how someone navigates through their contacts; a chart in an annual report tells the story of how well the company has performed in the past year. Time is integral to telling comprehensible stories, because it allows for a beginning, middle, and end. Animation in our interfaces connects the dots for users in a very direct way.
Mac OS X's stacks feature: Collections of icons "stacked" on top of one another. Their visual utility is limited when still, but the story is clear once you see* the pile expand.
Unsurprisingly, information graphics and data visualization gain a tremendous amount of explanatory power with the addition of time (and motion). A print publisher that has embraced the extra dimensions that come with online publishing is the New York Times. Their interactive graphic features often contain information that would be challenging to explain in paper format.
By increasing the amount of data displayed while telling a more fluid story, time (and motion) can offer an opportunity to add depth _and_ clarity, simultaneously. What are other good examples of integrating time as an additional dimension?
* It's tempting to assume that the interaction is clear for our users because it is clear in our own minds; but not providing a cohesive story (i.e., showing the animation) makes understanding difficult.