Websites publish lists of updates called "feeds" that indicate when new content has been posted.
When you subscribe to a feed, Google Reader starts monitoring it for updates.
You don't have to give any personal information, it doesn't cost a dime and it's easy to unsubscribe.
New content posted to your subscriptions will appear in Google Reader, the same way that new emails addressed to you show up in your email account.
This way, you can keep track of all your favorites sites in one place, without having to visit each one individually.