A genus (pl genera) is a group of species that share similar traits. For example, the modern chicken that so many people like to eat is a species within the genus of Gallus, which also includes several different species of junglefowl. The extinction of a species is horrible enough, but the extinction of an entire genus is even worse. In 1914, when the last passenger pigeon died, it also was the end of the genus Ectopistes. Nearly all extinctions are the result of human activity and almost all of that is from loss of habitat and and the vast majority of that is to clear land to graze or feed animals that will die to end up on people's plates.
If we can ever hope to slow the Sixth Great Extinction Event, we need to get everyone to stop eating animals.