What exactly IS divergent thinking.

Divergent thinking, as described by Robinson, isn't creativity. But he states that it is an essential capacity for creativity. It is defined as the ability of a person to see many different answers to a question and many different possibilities to define it. It is a capacity to think laterally and divergently (vs. linearly and convergently). 

What does that mean exactly? 

I think that the key thing about divergent thinkers (according to the definition) is that they do not accept assumptions readily and consistently think about ways in which what is taken for granted is questioned. It should be a mindset that is not just comfortable in ambiguity but thrives in it. In spaces where ambiguity exists (or encouraged), divergent thinkers can thrive. Perhaps the most important part about the mindset is that it can either be suppressed or mindfully cultivated. A divergent thinker may not just accept things as they are but will try to challenge the assumptions that exist.

The reason why it leads to creativity is that in order to think creatively, we often need to ask the question "what if..." or "why is it like that" in order to create something new and/or novel. Creativity, if nothing else, is the questioning or rejection of the status quo. 

So to see how it all fits into education, one needs to figure out IF divergent thinking is a necessary skill for the future. 

I would guess that in a world where efficiency and expediency is paramount, divergent thinking individuals would be largely problematic. For a community where compliance is necessary and where thinking too much will cause efficiency to drop when things just work, divergent thinking will gum up the works and cause things to get messy. You do not want a worker on the assembly line asking too many questions if the work is already well defined. 

It is when things get ambiguous and unknown, a little more necessary. For problems without a solution (or with problems caused by the current status quo), divergent thinking individuals suddenly become a lot more important, because these are the people who will come up with the innovative solutions. 

In a world where things are becoming more ambiguous or uncertain, divergent thinkers might be necessary IF the status quo is not working. More on this later.