1. The principal church of a bishop's diocese, containing the episcopal throne.
2. A large, important church.
3. Something that resembles a cathedral, as in grandeur or authority.
1. Of, relating to, or containing a bishop's throne: a cathedral church.
2. Relating to or issuing from a chair of office or authority; authoritative.
3. Of, relating to, or resembling a cathedral: tall trees whose branches met to form cathedral arches over the path.
a. A public building of ancient Rome having a central nave with an apse at one or both ends and two side aisles formed by rows of columns, which was used as a courtroom or assembly hall.
b. A Christian church building of a similar design, having a nave with a semicircular apse, two or four side aisles, a narthex, and a clerestory.
2. Roman Catholic Church A church that has been accorded certain privileges by the pope.
Here is more information about cathedrals:
And here is some more information about basilicas: