I'm having trouble understanding what I'm am granting to sites when they have "Authorized Access to my Google Account."

This is how I see what has authorized access:

1. Log into gmail.
2. Click on the link that is my name in the upper-right corner, and from the drop-down select Account.
3. From the list of links to the left, select Security.
4. Click on Edit next to Authorized applications and sites.
5. Authenticate again.
6. At the top of the page, I see a set of sites that have authorized access to my account in various ways.

I'm having trouble finding out information about what is being told to me here. There's no "help" link anywhere on the page and my Google searches are coming up unproductive. From the looks of what I see there, Google has access to my Google calendar. I feel comfortable about that, I think. But other sites have authorization to "Sign in using your Google account".

My question is, what exactly does that authorization mean? What do the sites that have authorization to "Sign in using my Google account" have the power to do? I hope that this simply means that they authorize using the same criterion that gmail does. I assume that this doesn't grant them the ability to access my email. Can someone please calm my paranoia by describing (or simply pointing me to a site that describes) what these terms mean exactly?

Also, if you have any thoughts about the safety of this feature, please share.

Thanks!