Ok, when you get your phone, it comes with all sorts of funky hardware which is capable of doing great things, like connecting to wifi, recognizing multiple finger gestures, take video using the cam, etc.
Carriers like sprint, tmobile, verizon, att and everyone else love to "lock down the hardware" so that if say you want to use your phones wifi chip which was ALREADY on the phone you paid for, a company like SPrint may want to charge you for enabling such "features".
So big bad SPrint wants you only use certain features on this device you paid for, but wants to charge you for features which you actually paid for and your phone is capable of. So what does "rooting" do? Rooting breaks Sprints barriers and 'restrictions' on your devices hardware, and allows you to do things like connect to a laptop using your phones wifi chip WITHOUT paying Sprint, you little devil! HOw could you??
SO theres this argument, whether some features should be blocked on phones hardware, as the customer already paid for the device, and SPrint wants to charge you $30 for something your phone is already capable of.
MOst common reasons to "unlock" these super-user permissions, are to :
--delete carrier bloatware, like SPrint TV, Verizon Apps, ATT SHitapps...
--Use your phone to connect to 3g/4g/Edge and share the connection with your laptop/Tablet WITHOUT paying the carrier a monthly fee.
--Install some applications not available in the Android Market.
--INstall different user interfaces (UI's) other than that your phone initially came with.
--Unlock more hardware features, like HD recording on some devices.
ALso, If you ever heard people 'jailbreaking' apple products like iphones and pads, its the same thing for Andoird devices.
so rooting is to android is what jail-breaking is to apple.
Personally, i think it should all be called jailbreaking to avoid confusion and keep the peace.