Rooting allows applications that require root user permission to run. Because of this, it allows you to have a lot more choice over how your phone looks, and you can also overclock the CPU inside your phone with SetCPU, if you're that way inclined.
rooting your phone is usually done when you want to run "roms" which are a whole new gui interface. think about what the htc interface/skin looks like this is called "sense ui". roms have their own "ui" so some look drastically different but still retain the same basic android code (although often improved).
with a custom rom you can also chose what kernel to use. i don't understand the whole concept as well as i'd like to but some kernels can greatly improve efficiency (and battery life by +50% or more some people state) over stock.
as dantdj stated, unlocking your phone allows you to gain access to your phone in a whole new way. the downside is that if you truly do not know what you are doing there is a chance you can brick your phone. its best to get at the very least, moderately familiar with everything before attempting if you dont want any issues.
if you want to change the look and feel of your phone without risking your phone to bricking then there are options out there that will let you change your homescreen, appdrawer without rooting your phone.
i have a htc droid incredible 2.2froyo which i left stock (at least for now). you would think its running a rom based on the desktop but its a few simple apps that let you have a decent amount of control.
to change the launcher bar (the one on the bottom with the app drawer button) there are a few apps out there to choose from with different options for each of them. just search the store for "launcher" and you will see a few. my personal favorite is "go launcher ex" it is free and gives you the most/best options of all of them. i have the bottom menu as a 3-part section which scrolls like the desktop does (except independent). it also allows you to have swipe up/down/touch actions for each icon you put on the bar which means one icon can have multiple uses. how nice! i also have it linked to a folder app which when i press a button on the bar brings up a screen with apps seperated by catagory, i'll explain that next
folder organizer lite is a free app which lets you put a "designation" on every app which lets you create folders for them. you can either place the folders on your desktop (or put them on bars such as the one in go launcher ex.
Desktop visualizer allows you to change the default icon "grid" size to one of your choosing. i'm unsure of what my default was, i think it was 4 wide by 4 tall. i changed this to something like 5 wide by 6 or 7 tall. all the icons are resized as well as widgets. the app also allows you to custom size/place widgets so you can have an overlapping effect if you so wish.
widgetsoid is a neat little program that allows you to create what i would call "control bars" which put commands like wifi on/off, gps on/off, sound volume control, screen brightness, etc onto one widget which saves alot of time if you access these functions alot. it also supports putting the bar in your notification area dropdown (the one you swipe down from the top) so you can access it anytime you wish without taking up desktop space. neato!
as far as customizing your desktop by now you should know the appmarket is flooded with customization widgets. we all have our own preferences when it comes to these, personally i prefer minimalistic appearances.
hope that gives you some insight into what rooting is and what it can do as well as some options that allow you to have a phone that looks different from stock but remains stock. just be sure you're familiar with the topic if you want to root. the non-rooting i mentioned can be done by anyone, even if you know nothing about android.