What is the difference between Sitecore's core, master, and web databases?

Question

What is the difference between Sitecore\'s core, master, and web databases?

Answer 1

Some great answers here but it's worth a clear note that the Web database is the default publishing target and is not set in stone. You can rename it to whatever you wish as well as have multiple publishing targets similar to 'Web'.

e.g. We have a Sitecore instance with two websites (website and intranet), thusly the Master database contains all the items for both sites. For publishing we have two targets 'Website' and 'Intranet' that are hosted by different SQL servers.

Ultimately our connections include: Core; Master; Website; Intranet (the latter two being copies of the original 'Web' database of course)