Fustat was the first Arab capital in Egypt. It was founded in 641 AD, after the Arabs conquered Alexandria. The Arabs did not want their capital to be so far away as Alexandria, which is why they made Fustat, which was closer, and was on their side of the Nile river.
Fustat became a beautiful and powerful city for over 500 years, but then it was destroyed during a war, when its vizier Shawar told his army to burn the city. Shawar did not want anyone else to capture the city, so he burned it instead.
Today there is not much left of Fustat, but some buildings can be seen in Old Cairo.