In this forum there's an all things root subforum you can check that out for detailed information, but to make it as simple as possible coming from someone who is by no means an expert.
A rom is an android operating system, like windows 7, or Linux or mac.
Android has froyo, gingerbread and many others. The two most popular ones for the optimus m that I am aware of are there sense ROM which runs froyo and the cyanogenmod 7 (cmod7) ROM which is a newer gingerbread ROM but still under beta and has some bugs, I personally use sense and love it. If you are rooted it literally takes minutes to install.
There are a lot of benefits like passing all of your apps to the sd, overclocking, customization and much more, you should really look into it.
I installed a custom ROM on mines a couple days ago with the help of the people in the forums I have been able to customize it to my liking and feels a lot smoother than the stock ROM. Wish I would have done it sooner.