NOUN (3)

1. the era of Islam's ascendancy from the death of Mohammed until the 13th century; some Moslems still maintain that the Moslem world must always have a calif as head of the community;
- Example: "their goal was to reestablish the Caliphate"

2. the territorial jurisdiction of a caliph;

3. the office of a caliph;

The Collaborative International Dictionary of English v.0.48:

Caliphate \Cal"i*phate\, n. [Cf. F. califat.]
   The office, dignity, or government of a caliph or of the
   caliphs.
   [1913 Webster]

WordNet (r) 3.0 (2006):

Caliphate
    n 1: the era of Islam's ascendancy from the death of Mohammed
         until the 13th century; some Moslems still maintain that
         the Moslem world must always have a calif as head of the
         community; "their goal was to reestablish the Caliphate"
    2: the territorial jurisdiction of a caliph
    3: the office of a caliph