Sometimes, it depends what is contaminating the water. Boiling kills many common bacteria like salmonella and e-coli so water centers will send out boil advisories if they detect those types of contaminations and you will be fine in that case. Sometimes it isn't bacteria themselves that make you sick, but the waste products and those will remain after boiling (especially common if the water was stagnant). Sometimes water is unsafe because of chemical contamination and that is also unaffected by boiling.

Some bacteria and viruses can survive boiling, so it is more of a reduction of risk rather than truly making it safe.