In Mexico the government has their own health care system, if you are a Mexican citizen you have access to it for free (if you are a student or you work legally), it's sustained by taxes that employers pay to the government, there are two health care systems IMSS and ISSSTE, depending on if you work for the government you get one or another.

These institutions will give you the treatment that you need and surgerys as well, except cosmetic stuff. Since these institutions aren't optimal (usually takes a long time to get attention) you might prefer to use a private health care, and you just pay a private company for what you need or pay monthly for an insurance plan, which will cover certain hospitals and specific diseases