Why a "Breeder Reactor" is called by such a name?
Suppose used Uranium rods which contain only U-238 are kept in or around a Uranium-reactor core. Also suppose the geometry is such that out of the average 2.5 neutrons produced in a fission, one neutron is absorbed by a U-238 nucleus in these rods resulting in Pu-239. Then we produce as much nuclear fuel in the form of Pu-239 as we consume in the form of U-235. If more than one neutron can be absorbed by these U-238 rods per fission then we produce more fuel than what we consume.
Hence we have a breeder reactor which generates nuclear fuel.