A ROM is a custom built version of the Android OS. It could be built directly off the Android source code or it could be a modified version of the official Android OS put out by your device carrier.
In order to run a custom ROM you have to be rooted. What is rooting? Rooting is when you perform a few special steps to obtain & grant access to the system level portions of your device, kind of along the same lines as having Adminstrator access on your computer in Windows. The OEM's and/or carrier don't like for you to have access to these areas because if you do something wrong it could brick the device and in turn people want to claim warranty on the device to try and get a new one which costs the carrier/store/OEM money.
Why do people do it? Well to be able to run custom ROMs, remove bloatware, run custom kernels (main reason to control processor speed for better battery life) to name a few main reasons.
Is it safe? Yes if you properly educate yourself on the terminology and techniques used to do it.
Does it void my warranty? Yes while your device is in the rooted state the warranty is voided. But there is always a way to " un root " the device in the event you want to go back to stock or need to have your device serviced.
CWM (ClockWorkMod) is a custom recovery on the device. The stock recovery is used to update/flash/install " official/approved " software updates. You can also reset the device (factory reset) from stock recovery. A custom recovery is placed on the device during the rooting process so you can flash/install " unofficial " software like ROMs, kernels, etc. It also allows you do do many other things like make a full backup of your device, wipe " clear out " the devices cache/data/dalvik partitions of the device and many other useful tools.
I mentioned that you need to find a ROM specific to your device/carrier. This is VERY important. You need to make sure if you attempt this to find/locate a ROM that is specifically made for your version of device & carrier because if you install a ROM from say " AT &T " and you have a " Vodaphone " phone there is a good chance the radio/modem software can hard brick the device. Again, taking your time and educating yourself on these things before doing anything is the best approach.