root is the user account in Linux with all privileges. The root user can edit anything on the system. For safety reasons, users do not have all those privileges. When you root your phone, you will gain write access to areas of the phone you couldn't previously access and are allowed to run more commands in the terminal. Because applications do not get a lot of priviledges, some of them require you to root the device in order for them to function properly (or fully). There is a tutorial for rooting in the Post #2 and there is a OneClickUtility that supposedly works on all firmwares here.
If all of this means nothing to you then you are probably wise to NOT root your phone. Mistakes using root can break your phone very easily. (Usually, but not always, these can be solved with a reflash)