Everything rooting allows you to do has been pretty well covered but I would like to take a minuete to try to break it down to a more noob friendly level.
First off root gives you full access to the phones system files that are other wise locked. This, as you know, allows you to add custom roms. Cyanagon Mod(CM7) was linked to above. This is w what I am running on my Droid 2 Global at the moment. It gave me gingerbread(Android 2.3) while the phone comes with Froyo(Android 2.2). Cyanagon used a clean untouched version of android as its base. Manufactures like Moto, in your case and mine, add Motoblur integrating it in to the very basic android source code.I personally liked Motoblur, but I can sync my contacts with Facebook anyways. It is not as fancy as Motoblur such as not displaying status updates when you click a contacts name, but it still syncs there profile pic which was the main thing i liked in motoblur anyways. Samsung adds TouchWiz UI to the android source code. HTC adds Sense UI to there phones. This more or less makes that manufactures phone a bit more unique then there competition. Since CM7 is based on vanilla android as it is usually referred to, it does not have a custom UI to hog up system resources. The devs take vanilla android and start molding and hacking at it optimizing, tweaking and adding features.
Now that is more about ROMs then rooting, but rooting will allow you to install a "recovery" software that then lets you flash roms, but also it allows you to make a mirror image back up of your phone to restore if you mess something up.
Root allows you to use special apps Titanium Backup(TB), as mentioned above, which backs up all user apps and data. It can back up system data/apps to. Now starting with Froyo, Android syncs this data with the market, and will allow you to auto restore your apps from the market if you ever do a factory reset for example. However, this process will always take longer then TB because you have to download and install the app. With TB, you are simply pulling the files from your phone. Plus it restores the apps one by one where as the market does it many at a time and can slow the phone down since it will be downloading and installing multiple apps at once. TB could lag the phone to but again, its faster.
You can use Ad blocker apps, but I generally prefer not to. Typically the in app ads are not in the way causing no problems. I try to support the devs when possible.
You mentioned other markets. Well there are several. Some legit, and some are warez. None of these actually require root access to use.I will not name any warez markets for obvious reasons, but there is, for example, the SAM(Slide Me Android Market) which is a free app and the apps and games it provides do not have to adhere to any of googles policies. This does not mean they are offensive,warez related, or anything else negative. For one reason or another they prefer to use a different market.
Rooting also makes it easier,although i think it can be done with out root but it requires knowledge of using command prompt to manually type in commands., to install inverted apps if they are system apps. For example a black and blue market:
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Black and Red market:
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Blacked out Google Voice:
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And so forth. Again root is not always needed, but generally makes it easier if the app is a system app like the market.