The Red lands were the deserts that protected Ancient Egypt (on both sides) from invading armies and influences from other countries. It also provided a source of precious metals and semi- precious metals.
Black Lands
The Black Lands were literally the Black Lands. After the Nile flooded on it's regularly predictable course it would left behind slit, which allowed fertile land for crops. But this was the only land in Ancient Egypt that could be farmed because of the thick layer of rich black silt that was only deposited when the Nile flooded.