How does meningitis kill your kids?

Depends on variables. Depending on the germ there are a variety of possibilities. Meningococcus can cause blood poisoning, low blood pressure, system failure and shock. HIB can do the same, cause brain abscesses, inflame the heart and lead to shock. Pneumococcus, tuberculosis and other germs can and do overwhelm the patient if untreated.
Brain damage. Meningitis is inflammation of the meninges, which are the layers of tissue that line the brain and spinal cord. Meningitis can caused by viruses, cancer, chemicals, bacteria, trauma, etc. The type that most people fear, that we vaccinate against and that you hear about in the news, is usually bacterial. When caught early, it can often be cured. When not, it can lead to brain damage or death.