In linux operating systems there is a user called root or super user. This user has access to everything including files critical to the operating system. When you are root you have power but you also don't have a safety net.
In terms of phones you normally gain root access to simply uninstall the operating system the vendor placed on your phone and install your own operating system either the version of android that google distributes or a version that someone has customized.
The benefits of custom installs could be anything it all depends on what features they've added but it also comes with risks in that these are generally not warrantied by any company.
The benefit of installing the google distro is a swifter update. In the case of your droid 2, for example, motorola and verizon teamed up to create the version of android 2.2 that is running on your phone. Some day google will release android 2.3. When that day comes both verizon and motorola will have to work together to create a version of 2.3 that they deem acceptable for your phone. This process has been taking months for most phones to date. The other advantage is that most of these operating systems developed by motorola, samsung, or htc all have some bloatware (ie the blockbuster app that you've probably seen). Sometimes these apps can't even be uninstalled from your phone so if you are able to install google's version you can free up some space because it doesn't come with that crap.