finger bowl

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A small bowl that holds water for rinsing the fingers at the table.

from The Century Dictionary.

• noun A bowl or glass for holding the water used to cleanse the fingers at table. Also finger-glass.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A small bowl of warm water placed at each seat at a fancy dinner for the guests to rinse their fingers with between courses.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun small bowl for rinsing the fingers at table