What is Origami?
I rather like Joseph Wu's "a little vague" definition of origami as "a form of paper art where folding is the primary technique to achieve an effect". This just about says it all.
I have agonised over "What is Origami?" for well over thirty years now, without coming to any conclusion. If I have seemed to have approached a conclusion, it is that no conclusion at all is possible! Nevertheless my ruminations have been very profitable in helping me to understand the nature of paperfolding. Sometimes the journey is more important than arriving. I have to say that my ruminations have greatly benefitted from John Smith's Profile of Paperfolding.
My only comment on Joseph's "loose" definition is that in one respect he is, perhaps, too precise. He refers to "Paper" folding, whereas the folding process can also be applied to other materials. Those that come to mind are metal foil, textiles, leather, sheet metal and even food, such as pancakes. No doubt other people will think of other media.
Because it does not apply to either art or craft, I exclude here, folding as it applies in the field of natural science. But it is still folding and it is relevant to the folding of geological strata, to flowers and leaves emerging in the bud and to the buckling of stuctures under pressure - see "Origami Science and Art", the Proceedings of the Utsu Meeting of Scientific Origami, which is a remarkable resource for expanding one's ides about origami..
I don't wish to push it to strongly, but a definition that I arrived at and which I think is comprehensive without being specific or judgemental is: "the art and science of folding".
But that is perhaps too sophisticated a defintion when the subject under consideration is the the merits of Hector Rojas's style of folding. As I often admonish myself, we should have our head in the clouds, but we must also keep our feet on the ground. Even with origami!