An article citation alert notifies you by email whenever a publication (e.g. journal article) you have chosen has been cited by a new publication that has been added to the database.
Databases like Scopus and Web of Science provide citation alerts for publications. Look for links such as 'Create Citation Alert' to create alerts.
An author citation alert notifies you whenever an author is cited.
Scopus database: search for an author and select 'Get citation alerts'.
Google Scholar provides the ability to track authors who have a Google Scholar profile. Go to the author's profile and click Follow to set up alerts to new citations to this author.
If an author does not have a profile, it is still possible to track individual papers by clicking the Cited by link underneath a result and then from the list of results using the Create Alert link on the left menu.