What is the importance of antimatter?

>As is known, I don't understand physics.
The front page of wikipedia links to new results in antimatter
related to antihydrogen.
https://en.wikipedia.org/wiki/Antihydrogen

>What is the importance of antimatter not counting nukes?

I'm not aware of any significance of antimatter in regards to nukes.  (neither bombs nor fission reactors; there are many potential fusion reactions; I don't recall if any produce a substantial number of antiparticles. )

>Why antimatter is accepted by the standard model in physics, but
anti-time and anti-space appear to be considered cranky topic?

The anti-electron (aka positron) was predicted in 1931 by Paul Dirac.   https://en.wikipedia.org/wiki/Positron   It was actually discovered in 1932, presumably as a spiral in a cloud chamber.   (It would be circling similar to an electron, because it has the same mass, but in the opposite direction, since it has a positive electric charge, in the static magnetic field applied to the cloud chamber.)

 You ask why it is "accepted":  Generally, things that are found tend to be "accepted".   What's the alternative?

For years, it was speculated that the Big Bang 'should' have produced equal amounts of ordinary matter and anti-matter, but despite this seemingly the vast majority of the known universe is ordinary matter.  (evidence:  absence of gamma rays that would exist profusely if electrons and positrons were continuing to collide and annihilate in today's world.)  

          Jim Bell