How does radiotherapy treatment work?

Damages tumor DNA. Radiation therapy uses high-energy x-rays to kill cancer cells. These x-rays interact with water molecules in the cancer cells, creating chemicals (free radicals) which damage its' dna. When tumor cells with damaged dna try to divide, they have a built-in safety mechanism that kicks in (called "apoptosis") leading to cell death.
DNA damage. Radiation deposits energy in the tissues and causes damage to the dna of targeted cancer cells. This interferes with cancer cell division and ultimately causes cell death when the cell damage is beyond repair.