CIA
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A 'CTR Importable Archive' file (or more commonly referred to simply as a 'CIA'), is a program file used by the Nintendo 3DS in order to preform a function. This includes games, developer applications, demos and many more.
A regular, encrypted CIA is importable to the Nintendo 3DS homescreen through title managers such as FBI, BigBlueMenu and DevMenu.
Encrypted vs Decrypted
CIA files can be either encrypted or decrypted for use with specific programs. While decrypted files can be used with both a 3DS unit and popular 3DS emulator, Citra; encrypted CIA files can only be used with 3DS units.
Another important difference between encrypted and decrypted CIAs is their filenames.
Files ending in .3ds are decrypted ROMs, installable through one of the aforementioned title managers, not to mention useable on Citra.
Files ending in .cia are encrypted, and can only be used after being installed on a system again, using one of the aforementioned title managers.