The term dirty ROMS is backwards-derived from the 32-bit clean ROMS that were built into later Macintoshes. That is, they didn't plan to make dirty ROMs. A ROM is a read-only memory chip built inside the computer. It contains permanent and unalterable software to help run the computer.
Well, in certain models of Mac computers-the Mac II, IIx, IIci, and the SE/30-the engineers and software programmers utilized a certain part of the ROMS for this or for that; it was a part of the ROM that nobody thought anybody would ever need ... Lo and behold, technology developed that needed that certain part of the ROM.