Hello and welcome to AF.
Rooting is basically hacking your android device and gaining access to every part of your phone including parts that you're not allowed to get to.
You can change/remove the OS (Operating system) and add a totally new one to your phone giving it a whole new flavor. You can also remove carrier bloatware and can get root only apps that can allow you to move apps to the SD card that would normally not allow you to move them there. You can make your phone faster or slower if you want to conserve battery life and making it faster makes it more zippy, but beware for doing this can damage your phone if you make it too fast.
You can also get free WIFI tethering too, but your carrier might catch on and charge you. You can even get different versions of android like ICS if you know your phone will never get ICS, then this would be a way to do so.
Pretty cool huh? Well, you should always do your homework before you attempt rooting, because you can run the risk of bricking (breaking) your device turning it into an expensive paperweight if something went wrong or you did something wrong.
All the above is just an example of what you can do after you root your device.
You basically become the Administrator of your device and you move up from average user. So please do your homework, for I would hate to see you brick your phone if something went wrong.

Here's the link to your device All things root section
Samsung Admire: All Things Root
Guide (5/22/2012 ongoing) where you can ask there about it and get the best info.