The grass and shrubs are shown because Oasis' occurs "where fresh water is available." Plants, shrubs and grass all need water in order to survive. Somewhere that contains a lot of water will have plants.
The large areas of land is the Oasis itself. This are of land has a lot of land/water for plants and vegetation. It is very fertile land.
The water for the vegetation is shown because it was said that Nomads went from oasis to oasis on a thrive for water.
The dates and peaches are shown here because Oasis dwellers often grew fruits like the dates and peaches.
