I'm not sure what rooting is, but I'll take your word for it because you know your tech stuff. 
Rooting is a linux term (since android is based on linux). Basically the closest anology to Windows would be if you were to become the SYSTEM user (open up the task manager and see how many processes were started by system). It allows you to remove any crap from the OS that may be preinstalled as well as in general just tweak the phone to precisely your needs, allowing you to get the best battery life or performance.
In layman' s terms, what does it do? Does it void the warranty? Is it safe?
Rooting, at least around here, no one gives a crap. Installing custom roms is another matter, and generally will void the warranty.
And I'll also assume then that the battery life is not good? My moto lasts for 3-4 days.
It depends, but smart phones in general don't have great battery life. Getting 3 days of moderate use out of it is pretty much the best you can hope for. Some are worse than others, but thankfully there are a lot of things you can do to improve battery life (disable 3G and disable wifi whenever you aren't using them is a real biggie)
