The Red Waste is a desert region on the continent of Essos, located thousands of miles to the east of Westeros. It is located south of the Dothraki Sea and Lhazar, northwest of Qarth, and east of Slaver's Bay. It is a harsh sandy wilderness that even the Dothraki fear to cross.
After pillaging the lands of Lhazar, the Dothraki khalasar of Khal Drogo skirts the northern edge of the Red Waste. It is in these border regions where Drogo falls from his horse and his khalasar scatters, and also where Daenerys manages to hatch her dragon eggs..
Daenerys and her retainers travel across the Red Waste in search of succor. After Daenerys's horse dies from lack of water, she sends three of her bloodriders in search of civilisation. Ser Jorah Mormont tells Daenerys that he has not been as far east as the Red Waste, but he has heard that it does have an end and it is possible to cross it. One of Daenerys's bloodriders, Rakharo, is executed by a Dothraki khalasar and his head sent back to her.
In the books
In the A Song of Ice and Fire novels, the Red Waste is extremely large, taking weeks to cross, and is unrelentingly hostile. Water is scarce and food sources almost non-existent. The wasteland is located east of Slaver's Bay and west of the Jade Sea. The city of Qarth lies southeast of the waste. Its southern edge runs along the Summer Sea. There are ruins in the waste, suggesting that at one time it was much more pleasant and habitable than now. One such ruined city is called Vaes Tolorro, the City of Bones.
The Red Waste is not strictly speaking a true "rolling sands" desert, though it is a "desert" in the broad definition that it receives virtually no rainfall. It is actually far more harsh and dangerous than even a dry sandy desert, due to its low rocky hills, barren windswept plains, and dry riverbeds. It is more of a blasted wasteland than a simple sandy desert, which explains why it is known as the "Red Waste" and not simply the "Red Desert".