MCC / MNC
The Mobile Country Code (MCC) and Mobile Network Code (MNC) fields together specify which carrier you are using. Each carrier in the world has their own unique MCC and MNC value pair.
These will usually be set according to the SIM card that is inserted in your phone and won't need changing. Your device may even prevent you from making changes to these fields, rendering them display-only fields.
Android's APN settings are all carrier-specific: when you create an APN setting, it'll be used only when you are using the carrier network specified in its MCC and MNC fields. If you take out the SIM card and replace it with one for another carrier, the APN settings you previously created will probably no longer be visible. If so, this is not because they have been deleted, but because Android sees no need in showing you APN settings for networks that don't match your SIM card. In reality, Android devices usually ship with a large number of pre-configured APN settings, but only the ones that match the MCC and MNC corresponding to the provider of your SIM card will be listed.
Changing the MCC and MNC fields for an APN setting is not recommended (if your device allows it). Instead, if you want to configure an APN for a different carrier, it's recommended to insert a SIM card that corresponds to that carrier first.