To "Check out" an ebook, you DO need Adobe Digital Editions. Checking out the ebook means that you are reserving the use of the ebook for yourself alone for a certain period of time. It is most useful in the following circumstances:
In order to check out an ebook, you must first:
Click on the link above to download the correct installer for your computer.
After installing Adobe Digital Editions, you must "authorize your computer" or device. If the installation process does not automatically prompt you to do this, go to the Help menu and select "Authorize computer".
Here's a screenshot of the Windows Authorizing your computer menu: