Or is it just a fashion invented by the rubber merchants to sell more rubbers ???
Basically it is the combination of a topsheet with "Chinese" pimple geometry (mostly to some degree sticky) and a dynamic "Tensor" sponge, to rival a boosted Chinese rubber. Simplified, of course, but this "best of both worlds" approach was sometimes used in the marketing as well.
As on top level boosted H3 is the benchmark, early hybrid rubbers were mostly fairly hard and not easy to play for many. But the trend caught on and soon enough hybrid rubbers with softer sponges appeared.
The closer a hybrid rubber plays to a "normal" rubber, the more some people doubt it is a hybrid at all. Take for example Andro NUZN, which is only slightly sticky, feels more alive than many other hybrids, even more alive than some normal Tensor rubbers, hence the claim "that is not a hybrid" by some people who tried it. Well, Andro disagree ;-)
Yet I have also seen claims that some newly released rubber is a hybrid rubber, maybe because it wasn´t too bouncy, and yet it´s "just" a new normal Tensor.
Maybe you can find some information on what this pimple geometry actually is, it has something to do with the form of the pimples etc., but I am not technically inclined enough to explain.
On the new Omega 8 series, XIOM claim that the Hybrid is
"Hybrid of Tension Rubber & Chinese Sticky" while the China version is
"X FACTOR Sticky for Forehand Drive".
Considering Omegas are manufactured in Germany a "Chinese" rubber doesn´t have to be produced in China. ;-)
Confused?
At the end of the day, a fast sticky rubber can be a fast sticky rubber without being a hybrid, a German rubber that hasn´t too much of a catapult effect can be a hybrid, but doesn´t have to, and so on...
Maybe that´s why most companies have Hybrid in the name of their rubbers. The one that kinda started it all (dignics 09c) doesn´t and the term never appeared anywhere I think, same with NUZN.