A domestic flight within Egypt is a flight that flies between destination within Egypt, for example, Cairo and lands at another destination in Egypt, for instance, Hurghada. As the flight doesn't leave the country, the flight will be considered a domestic flight because the departure destination and arrival destination is within the same country.
As domestic flights mean you don't leave the country, you won't be subject to border and immigration controls. Also, carrying a passport may not be required. However, you will still need a valid photo ID, so many people choose to use their passport anyway. Those residing in Egypt or have a reference with Egypt from outside of the country can use the Egyptian Identification card instead of using a passport to travel within the country.