A unit of government created by and under the authority of a higher level of government. If a state divides itself up into counties, the counties are political subdivisions of the state. If those counties divide themselves up into county subdivisions, the county subdivisions are political subdivisions of the counties, which are in turn political subdivisions of the state.
In BCAT usage, “political subdivision” typically to refers to any type of jurisdiction within a state or territory, but not including the state or territory itself.