It dissolves from the soil into the soil and ground water and the plants cannot take the saltiness of the water, so they don't grow. It becomes pretty much as if the fields were irrigated with seawater. Not a good thing for land plants. How long it takes to wash away the salt is hard to say in detail, because it depends on how much rain the area gets every year, how much salt was put in the soil, and how much the water runs way rather than evaporates (if there is a lot of evaporation, the salt won't be leaving fast at all). North Africa is a relatively dry area and has a high evaporation rate, so desalination of the soils would likely take centuries.