Welcome, mikeg! Glad to have you with us! Make yourself at home and jump right in! Everyone is here to help and learn! Reading the threads on the forum will only increase how much you enjoy that new Droid! The possibilities for customization are endless!
Basically a widget is a way to manage a program or its elements without going into the program each and every time to accomplish the same thing. Applications are programs on your Droid. If they don't come with a widget - and many don't - you can create a shortcut to that application on one of your homescreens for much the same purpose as a widget.
To move icons around, simply long press on the icon and move it wherever you want on the screen, or into the app drawer at the bottom of the screen to remove it altogether. I hope that helps! Enjoy your new toy!