What is this Ceramic Container?
Its a butter bell / butter keeper.  My parents have one.  You put water in the bottom, butter in the bell under the top/lid and that forms an airtight seal allowing you to keep the butter at room temperature. 

Here's one for sale showing both parts clearly.

http://www.kitchenandcompany.com/Storage-And-Cleaning/Countertop-Organization/Butter-Dishes/_/Norpro-4-Butter-Keeper?tc=gfs13&amp;utm_source=google&amp;utm_medium=cpc&amp;utm_content=Norpro%204%22%20Butter%20Bell%20Butter%20Keeper&amp;gclid=CM2C1ZSRmroCFSpk7Aodt3kAgw