Don't worry, ive been using these programs for a few years and still don't know or understand half of it.
Anyway, cwcheat (and other programs like it) are software that you install onto your psp. They basically edit the game's code to change different values or attributes in a game. In other (harsher) words, they let you hack the game's code to cheat.
To answer your second question, yes, you do need to "mod" your psp in order to use it. Your psp must be running a CFW (custom firmware) which is an operating system that lets you use programs like cwcheat, as well as other things not allowed by sony's official firmware. Now you cannot just update your psp to a CFW, you do have to hack your psp. The most common (and by far the easiest) way to do this is to make/buy a "Pandora's battery" and use a "Magic Memory Stick" to install the custom firmware. Then you can add cwcheat along with may other programs to your psp.
There are countless tutorials explaining how to install CFW on your psp along with installing CWCheat. I personally used TheUltimatePandoraPack as it shows you how to make a pandora battery as well as giving you a link to a magic mem stick autoloader (its worth it).
I can't seem to find a reliable download for TheUltimatePandoraPack. can anyone reccomend a free file hosting site (file size 42 mb) i could use? and i'll post the link here.