Welcome to the forum!
Quick answers to the words you listed:
Froyo = Android OS v2.2. For some strange reason Google decided to name each version of the Android operating system after a type of dessert. These names correspond with a letter of the alphabet for the order they came out. 1.6 being the fourth version was Donut, Eclair came next and it is the name for 2.0/2.1 which is now being followed by 2.2 or Froyo (Frozen Yogurt) and 2.3 will be Gingerbread which we should start to hear more about in the first quarter of 2011.
Root = There will be much better explanations found around the forum, but it is basically hacking the phone or gaining full access to it (depends on your point of view). Rooting opens the phone up for things like overclocking the CPU, custom themes, custom Roms and more. It really is limited only by what different developers are willing to try and what the phone can actually physically do. A good example of this would be "older" phones that are running modified versions of the latest software, which is something they were never expected to do. Rooting used to be more complicated, but some developers have actually created applications that can do it in a matter of minutes now. Warning, it will void your warranty.
