Wordpress.com is the easiest but most restrictive way to install and use Wordpress.
You are limited to the available templates (which you can not modify), you can not place ads are affiliate links on your site, you can not control the domain name URL.
The hosting IS taken care of for you so you do not need to install it on your own web server. They charge $15 a year for the domain name (which is pretty standard)
Wordpress.org is free and is where you go to download the files to install on your own web server. You have to pay for your web server as well as the domain name, however this method provides the most customization in templates and URLs.
.com is good for the very basic user.
.org is good for people who want control of their web site (or their clients)
I have installed and developed a few WordPress sites and always steer clients to go with .org
It just does not seem like YOUR web site until it's YOURS :)
