Darbouka is a Middle Eastern percussion instrument shaped like a bowl that can be made in pottery, or metal and cover with a Animal skin. The origin of this instrument dates back to the Babylonian antiquity, that is to say roughly 1100 before BC.

The goblet-shaped single headed hand-drum is an ancient drum. It was originally played in Egypt, Armenia and Turkey. The darbuka is considered to be the leader of percussion instruments in the Middle East. The origin of darbuka has its roots in the Oriental music, where distinctive rhythms are quite common.

However, in the latter years, Darbuka made its way into Western music. Authentic darbukas are home made and are made of clay or wood with goat skin stretched over the top using rope, leather thongs or nails. Contemporary versions of darbuka may be made of aluminum, copper or Fiberglass.See pictures below.
The fact that the drum is single-headed distinguishes it from other musical instruments of the family, such as the tabla, dhol and pakhawaj. Since the instrument has a long history of being used for belly-dancing music in the Middle East, it is also referred to as the belly dance drum.
Goblet drums are one of the most important broad classes of drums, played heavily across Asia, North Africa and Eastern Europe. These instruments have many similarities, and there are many similar names in use:

Darabuke, Darabuka, Darambuka, Tarambuke, Tarambuka, Darabukka, Derabucca, Darbouka, Derbekki, Drbekki, Drbakka, Derbocka, Derbouka, Dobouk, Donbak, Dombak, Tombak, Doumbek, Dumbelek, Darbuka, Deblek, Gedombak, Khalouze, Tarabuka, Tarija, Tablak, Toubeleki...
for more story on darbuka names and different types check these great sites:

Persian Traditional Music by Nasehpour Family
The Troupe - Doumbek, Tonbak, Darbuka, and Tabla