Mifare DESFire is a RFID Technology following the ISO14443-4 and has 13.56MHz. Its designed by NXP Semiconductors. For detailed information about how Mifare DESFire works, you need a NDA.
The protokoll depends on APDU´s. The cryptographic part of Mifare DESFire uses AES, DES, 3DES and 3DES3K, with max 14 Keys per Application.
Mifare DESFire is designed like a Filesystem using a root directory called PICC and underneath are Applications which contain Files. All Applications are addressable by Application-Id (AID), while Files do have Id´s. There are different file types like standart-data or backup-files.