What is the difference between the databases: Master, Core and Web?

I am looking at the Broken Link report - and am getting the same error in the Master database as I am with the Web database - and not sure where to go to resolve the issue. 

  • Resolve problems in the master or core. Database definitions are:

    Master
    The Master database is the authoring database - it contains all versions of any content or assets.

    Core
    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)

    Web
    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.