The Ultra Beast War was a war from hundreds of years ago. It started when ultra wormholes appeared, transporting Ultra Beasts to every island in Alola. They wreaked havoc, murdering, destroying property, and ruining Alola.
They were led by a black colored pokemon known as Necrozma. It is unknown what kind of pokemon it is. However, accounts say that the Necrozma had more power than it used, and that if it seriously wished for the quick destruction of Alola, it would have been able to do so. Considering this, there are no possible explanations for why the alien pokemon would have decided to attack a region of our planet.
The battle had been ended by the combined efforts of the four guardian pokemon of Alola, along with Sun, a pokemon trainer who is hailed as a legend for having caught a Solgaleo. After the war, he rode his Solgaleo to traverse space to find out more about the ultra beasts, but he has never returned. It can be assumed he died, which was a great sorrow for everyone.
The Ultra Beasts didn't all leave, however; some stayed behind after the war, befriending trainers on our planet. Professor Kukui of the Alola region designed Beast Balls, a new kind of pokeball that can capture Ultra Beasts, and shipped them everywhere worldwide. This allowed trainers to capture Ultra Beasts and battle with them. The Beast Balls are very expensive to make, however.