What is a read-write CD-rom?

Answer 1

This was mainly used to distinguish between different kinds of CDs, the (factory manufactored) read-only CDs, the recordable (write once) CDs and the re-writeable CDs.

'Read-Write CD Rom' usually refers to the last kind. Formally it's a misnomer, since ROM (read only memory) would exclude writing, but since CD-ROM was initially the most common kind, many people referred to CDs as CD-ROMs and then added distinguishing modifiers like 'read-write' without realizing the specific meaning of the ROM acronym.

(The same applies to read-write CD-ROM drives, named that way to distinguish them from read-only CD drives.)