Floodplain tiles have a base yield of +3 Food. The Lady of the Reeds and Marshes pantheon increases the yield of Floodplains by an additional +1 Production. Floodplains lower the Appeal of surrounding tiles by -1, and reduce the combat strength of defending units by -2 .
Floodplain tiles cannot typically be developed with tile improvements, districts, or most wonders (though Egypt uniquely ignores this limitation, and Nubia can construct Nubian Pyramids on floodplains). Floodplains with bonus, luxury, or strategic resources can be improved as normal.
Floodplains redeem deserts for city development, ensuring a supply of food. The trade-off is that - with the exception of Egypt due to their Iteru ability - floodplains are not acceptable tiles on which to place districts (other than the City Center) or wonders. The exception to this are wonders that specifically require desert tiles (Pyramids, Petra), which may still be built on floodplains. Still, the fact that Floodplains provide plentiful food in the middle of the desert is enough, especially when they happen to have Wheat or other resources on them! Use them exclusively for farming, and place your districts away from the River.
The effect of the Petra Wonder does not apply to Floodplains.
Since Floodplains (appropriately) are always lowland, there will never be Hills on a Floodplains tile.
Floodplains are low-lying areas adjacent to rivers, and prone to flooding each year (or more often) and hence fertile from soil deposits and some of the most productive farmland known. Perhaps the best known are those along the Nile, which helped ancient Egypt become one of history's greatest civilizations.