A PSP ROM is basically a copy of a game that can be downloaded from the Internet to your computer and then transferred to the memory stick to be played on your PSP. To play these games you must have the correct firmware, it usually means downgrading your PSP. You should be looking for firmware version 1.5, but do not worry I have found a place that not only has literally hundreds of ROMS for you to download but also all the information on downgrading your firmware. It even has step by step guides to help you all the way.
By the way if you want to find out what firmware version your PSP is running just turn on the PSP, go to settings> system settings> system information click X and you will get a message "system software version" 1.0 1.5 1.51 or 1.52.
As you know Sony decided to release games for it PSP using UMD or Universal Media Disc, which can store up to 1.8GB of various media types including, games, music and video. Sony has no intent of releasing UMD readers / writers to the general public. So in theory UMD's are non-writable.
There are also a lot of PSP games by unlicensed developers and game demos freely available on the Internet but you must be careful where you down from.
You will be surprised installing PSP ROMS is actually a lot easier than you might think. A lot of the time is a simple process of drag and drop. As long as you put everything in the correct folder you will be OK.
First of plug your PSP in to your computer using your USB cable. Turn on your PSP and find your way to Settings> USB connection and press X. You will find that your computer will automatically find the PSP. Go to my computer> removable disc (usually drive F :). You will now be browsing the contents of your memory stick. You will see a folder called PSP open this up and create a folder called GAME. Remember you will need to create a new folder for each ROM you use.