What is the difference between Sitecore's core, master, and web databases?
I recommend you look at the Launch Sitecore site to understand more about the CMS.
From the page on Sitecore Architecture:
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.
Of course, in an Enterprise deployment, you may have multiple Sitecore instances, which may share DBs (or not)