It's not really newly discovered anymore. It was theorizes over 100 years ago, and even got its name all that way back, but the real observations from cosmic rays, as well as the artificial creation of them has only really happened in the last few decades.
As for how real they are, keep in mind that we already use them to a certain extent for certain laboratory experiments, so it is widely accepted to be a real thing. I don't think anyone really objects to their existence anymore, and most people who are familiar with physics accepts them as real.
Antimatter is composed of antiparticles of regular particles. For example, the antiparticle of electron is called positron. It has the opposite electric charge and some other quantum numbers to those of an electron. They were theorized a long time ago and individual antiparticles have been directly observed in particle accelerators given rise to in high-energy collisions of particles. A particle and its antiparticle destroy each other in a process called annihilation which releases a great deal of energy.
Antiparticles can make up larger particles and structures such as anti-atoms or anti-molecules. In principle, there could be an anti-Earth or anti-you or anti-me. But there is a great asymmetry in the prevalence of matter and antimatter for the benefit of the former. It is one of the great mysteries of physics, Baryon asymmetry by another name, as to why this is the case. The standard theory of particle physics provides no reason for the asymmetry.