Resolve problems in the master or core. Database definitions are:
The Master database is the authoring database - it contains all versions of any content or assets.
The Core database is all Sitecore settings, as well as the tables containing the .Net membership provider (i.e. users/roles contained in the Sitecore repository)
The Web database is only the latest published version, and the content that is driving the live web site. Therefore it is a subset of the master database, optimised for size and speed. When content is published, or goes through the publishing task of a workflow, the latest content version is copied from the master to web database.