Like hieratic, demotic was a simple form of hieroglyphic used for everyday purposes. It was even faster to write than hieratic. Demotic means 'popular', and has the same root as 'democracy'.
Demotic was invented quite late in Egyptian history, about 700BC. That's about 600 years after Tutankhamun. It was the ordinary writing of daily life during the Ptolemaic and the Roman periods. The Rosetta Stone, made in 196BC, had a demotic inscription on it all about King Ptolemy the Fifth.
This is an example of some demotic writing. The hieroglyphic version is given below.
From Gardiner (1950), Egyptian Grammar.