Forma Migratoria Multiple, or FMM, is the official name for this document. It is a permit to enter Mexico that is only given to tourists. People call it a tourist visa, but it's a travel permit, not a visa. It can only be used for a maximum of 180 days. It is a one-time travel permit given to everyone, even children.
If you overstay your Mexico Tourist Card, you must go to an immigration office in Mexico or the immigration center at the airport and pay a fine. The amount of the fine depends on how many days you overstayed. Then, before you leave, you must plan to get an exit visa.
If you lose your Mexico Tourist Card, you can get a new one at an immigration office. You'll also have to pay a fee for replacing it.
If the tourist card was given to you for 180 days, you can't make it last longer. A Mexico Temporary Resident Visa is needed if you want to live in Mexico for more than 180 days. On the other hand, if the INM gives you an FMM with a shorter validity period than the maximum, like 60 days instead of 180 days, you can extend it to the full 180 days. You can only extend your tourist card while you are in Mexico.