UV-C is absorbed by DNA/RNA in microbial pathogens such as bacteria and viruses, and causing damage to their DNA/RNA, hence stopping their reproduction. Typically, UV-C does not kill microbes instantaneously, but inactive them, rendering harmless.
DNA/RNA in microbes have a peak absorbance around 265 nm which is well within the UV-C range. This explains why UV-C has a strong germicidal effect. The absorbance drops significantly as wavelengths are greater than 280 nm, i.e., UV-B and longer wavelengths.
See: Reference for more details.