In 'library-speak', a periodical is anything that is published on a regular basis such as a magazine. A periodical index points out where articles on certain subjects appear in many different magazines, journals and newspapers.
Back in the day, periodical indexes used to be compiled and printed in volumes. If your library has been around for awhile, you can probably find a couple of these older, dusty indexes. The Readers' Guide to Periodical Literature, those green volumes you may have used to find articles for your term papers, are periodical indexes too.
Now, many indexes are available online from your library. Some may only be available if you visit the library in person, while others are accessible over the Web. Besides the standard citation information, some of these newer indexes contain abstracts or even the full text of the article online.