A Powerful Run Time Environment For Users and Developers.
Adobe Air is Adobe's runtime environment (RTE). To the average user, it will bear similarities to Java, as it does much the same thing: it provides programming options to developers, which allow their applications to theoretically be run on any platform that supports Adobe Air. Users will not notice these enhanced development capabilities, but may find apps made in Air more useful. How much more useful, though? The answer is closely entwined with Adobe's old Flash runtime environment, and how useful you found that.
A Flash Of Insight
Adobe Air provides compatibility with Flash-based applications, from basic Flash games all the way to fully-fledged apps (and games) that run on your desktop, in their own files. For development purposes, it is new as of this writing and needs some tweaks and optimization, but it provides many more options than Flash itself did.
Out With The Old, Slide In The New
Air has many of the problems that early Flash suffered from: a lack of developer support making it hard to learn the runtime environment, and for the end user, apps made in Air can run slowly on older devices. It's undeniable, however, that Adobe Air provides a level of Adobe Flash compatibility that may not otherwise exist, on devices old and new, so if you have any investment in things made with Flash (or especially if you've developed with Flash before), try Air.