CPU modes are how the PSP runs; Below are The two CPU modes, and some PSP OS modes.

It Kernel Mode is able to run any code it is given. A bit like if you try to go into a restricted area in a federal building. You will be sent away. All it is, is extra resources, so you can make your code to run better and with less restrictions. Kernel mode also allows access to further restricted modules, allowing new and better things to operate. 


ISO loaders need kernel mode functions to alter the path of some I/O commands to a file, not a device, so the PSP thinks it is accessing the UMD drive, but it's just running a file off of the memory stick.

Exploiting or illegally accessing other modes means to forcefully gain access to all these extra sectors. This can be done by overflowing the systems OS, allowing restrictions to be obsolete.

User Mode is basically the 70% restricted mode that is practically useless to us.
Both User and Kernel mode are CPU or "Processor" modes of execution. These are what are used to run code.

VSH mode, which the TIFF exploits run in, is a sort of slightly more restricted version of kernel mode. It is usually only used in the XMB (Main Menu). The 1.50 Kxploit method also ran from VSH, but it ran from a place where code is normally fed to the CPU anyway, so it had no restrictions.
GAME mode has its uses, but has severe restrictions. It is what the the GTA ELoader runs in. It cannot use kernel functions, which means we cannot write to Flash0, alter device maps and running code from the new location, or anything like that.
UPDATE mode is almost completely unknown. It is not known what it can and cant do; But that is believed to be the mode that updates run in. Someone also managed to load a modified Eloader into this mode; But it was still basically GAME mode, with all the restrictions, but loaded a few different modules.
These modes are all PSP OS modes.

 

NOTE:  

The correct spelling of  "Kernel" has no 'a' in it. It's not called "Kernal", as a lot of people mistakenly call it.