In general, there are three types of alerts:
Search Alerts - You do a search on your subject (eg. William Shakespeare and television adaptations) and receive alerts when new articles have been published on the topic.
Journal Alerts - Receive an alert when the new issue of a journal has been published. Some journals send the Table of Contents (TOC) and some send the TOC and Abstracts.
Citation Alerts - If you are interested in knowing when someone cites a specific article, you can set up a Citation Alert. These are not available from all databases and publishers.