There are many formats for games. Here you can find out what to do with them, and more.
How can I install apps, DLC, or PSN games (PKG files) on CFW?
You can move package files to your console by either using FTP to place the file in /dev_hdd0/packages/, or by placing it on a flash drive. You can then install it using the Install Packages option on the XMB and selecting the corresponding folder. The app should then show up on the XMB in the respective column if it is meant to be launched. Keep in mind that if it is a DLC or PSN game, you will need to activate it using a RAP file and ReActPSN.
Where do I put my game backups (ISOs) on CFW?
Each ISO type goes in the respective folder on the hard drive (dev_hdd0). You may need to create them first: PS3ISO, PS2ISO, PSXISO, PSPISO, BDISO, DVDISO. Extracted PS3 ISOs go in GAMES if on internal, and GAMEZ if on the network or external storage.
Can I play on PSN with a CFW console, and if I do can Sony ban me for going on PSN with CFW?
Yes, if you're using a current CFW or one that is spoofed to the latest OFW version. Running any homebrew while on PSN, not preparing your console with apps such as PSNpatch, or modding on PSN can get you banned.
Is there a difference between folder format ("jb") and ISO format?
If the game is a 1:1 rip, it may be a lot smaller in folder format. Folder format games also allow the flexibility of swapping out files at any time, which is useful for loading game mods. However, ISO format is required for the following games:
Call of Duty: Modern Warfare 2
Call of Duty: Modern Warfare 3
Call of Duty: Ghosts
Call of Duty: Advanced Warfare
Metal Gear Solid: The Legacy Collection
How can I update my games?
While connected to the Internet (and signed out of PSN), you can safely update by hovering over the game, press Triangle, and select Update. Alternatively, you can do the same from within multiMAN.