Glad you asked.   I would of course be the last person to suggest it is any one thing– and I mean to use my website and blog to advance the conversation about what it is, and never to finally answer it.   Even this answer, as posted here, will change and evolve often.  

But let me offer a starting place answer: 
21st century K-12 education (or, in my shorthand, the lovely palindrome 21k12) is education that concerns itself with at least some of the following questions, and of course many others additionally: 
1.  How is our educational program attending and responding to contemporary research in educational best practices?     
As Marzano writes in his central and essential research on this question, instruction is increasingly a science rather than an art, and the research is now too good to be dismissed.   And brain research has advanced too far to be ignored.   So a 21st c. school is vigorously pursuing understanding of what the research tells us are the best ways for students to learn.   Now, this should never be a straightjacket, and Marzano himself, in one of my favorite passages, says it is for experienced and thoughtful educators to select and apply the research with a careful eye for contingent circumstances.    Besides Marzano, I am also especially interested in contemporary educational thinkers Grant Wiggins and Tony Wagner– but my list is not intended to be exclusive.  
2.  How are we educating for critical inquiry, deep thinking, and problemsolving?
Voltaire was hardly 21st century, but he said to judge a thinker not by his answers but by her questions– and this, I think, is more important than ever.   Again and again as I read about good teaching and learning, I am struck by the emphasis on questioning, on teaching that promotes not certainty but ambiguity and argumentation.  Teaching should problematize, and learners should approach topics critically, grappling with underlying “essential questions.”   Much of the quality of a high school classroom can be found in the quality of the questions teachers ask students, and students ask of their teachers, or each other, of themselves.
3.  How is our educational program attending and responding to the way the world is changing, and what we believe as a school will be required of our graduates for success on a fast-changing planet? 
Tony Wagner.  Dan Pink.  Howard Gardner.  Thomas Friedman.   Ray Kurzweil.  I realize that sometimes Dan Pink, one of my favorites, can be a bit glib and superficial.    But the key here again is not that there exist any certain answers to how the world is changing, or that any individual guide has the best directions, but a 21st century education is actively engaged, ongoingly, in the consideration of how the future will be different, and reviewing its own program for alignment.   This can be done is so many ways– even in totally fun ways by watching future-set movies– and then seriously grappling with how our program can best adapt to our view of the future. 
4.  How is our educational program effectively and richly utilizing contemporary 21st c. tools for learning?   
The Greeks used a great deal of memorization and recitation as learning tools, because they only rarely could use writing; schools quickly adopted blackboards when they first became available.   Good schools are always using the best current technology available to advance student learning– not to learn the technology, but to use the tools to advance the learning.   The tools of our age are digital: laptops, cellphones, podcasts, wikispaces, and many more.   They are powerful and wonderful tools, and should be thoroughly and appropriately integrated, into student learning in a seamless way. 
5.  How is our educational program one which advances sustainability and stewardship? 
Sustainability has become the central thrust of NAIS’s bold and vigorous leader, Pat Bassett, and he is right: it must be at the core of what we are doing as educators.   How is our school itself self-sustaining, and modeling a sustainable way of living.  How are our students learning the significance of sustainability, and how are they learning to be better stewards of our planet?
6.  How is our educational program one of “authentic learning,” where students learn by doing, and are active participants in their own learning, doing work that is significant in its own right?
There is just no excuse anymore, with the tools we have available and the understanding we have of learning, to educate primarily by worksheets, lectures, and multiple choice tests.   We learn to ride bicycles by riding bicycles, out on the street, with a helmet and a helping hand, but not in a classroom studying a diagram and answering questions about it.  And we never forget how to ride a bicycle, either.    We should be consistently asking ourselves, how is the learning transferable, and how can it be transferred to real world applications now– not in some abstract future. 
7.  How is our educational program one that is engaged with the wider world in an globalizing age?  
The IB program calls it teaching and learning international-mindedness; I think it can and should be linked to our longstanding commitment to teach appreciation for diversity and multiculturalism.    The World is Flat, the 21st century is bringing citizens of all countries ever more interdependent, and our schools have to be actively helping students learn to respect, appreciate, communicate with, and understand the deep meaning of global interdependence.  
8.  How are we teaching students to be innovators?  
Thomas Friedman is now beating this drum, and we can find it in Pink, Gardener and many others: the single most important trait for 21st century success will be the ability to innovate, something the US has long led in, but which is fast becoming the central global competition?  Let’s ask ourselves at each school: what do we mean by innovation  what can do to better develop it in every student, and how can we measure student learning of innovation? 
But don’t let me have the last word: use the response button below.  What other questions should schools be asking themselves to better promote 21st century K-12 education?  Where are my questions above off base, do you think?