Demotic was the everyday Egyptian script of the last thousand years before Coptic, a highly cursive and heavily abbreviated development of the older hieratic hand, itself derived from the hieroglyphs. It was fast, compact and extremely hard to read without training, and it wrote consonants only, in a system where a single group of strokes could stand for a whole word. It served administration, law, literature and religion in Egypt for centuries, and its last known inscriptions are from the fifth century of the common era, by which time Coptic was well established. The seven letters Coptic took from it are the direct link between the two systems, and kyima is one of them.
The relationship is worth stating carefully. Coptic did not evolve out of Demotic; it is a different kind of writing, alphabetic and fully phonetic, adopted from Greek. What it took from Demotic is a set of signs, not a principle, and those signs were adapted into the alphabetic system rather than carried over with their Demotic behaviour. The identification of which Demotic sign lies behind which Coptic letter is a technical question on which the literature is not uniform, and this atlas does not assert particular identifications for individual letters. That the seven came from Demotic is not in dispute.