It's used in 38 countries, including the United States. It was used for treating foods that had military applications. NASA has used irradiation extensively to sterilize foods that go into space. That's been done since the very first NASA mission in the early 1960s and up to the present. It really works much the same way that heating food kills bacteria.
Heat is just a form of energy.
Irradiation is a different form of energy. Irradiation is very effective inactivating all kinds of harmful bacteria. Irradiation is just using energy to kill bacteria. In no way does it impart radioactivity to the food that's being irradiated, so it certainly poses no risk to consumers. Irradiation has been endorsed by virtually every scientific body that's ever taken the time to evaluate its safety, including the American Medical Association and the World Health Organization.