Terrace farming is when farming is done on manmade terraces that have been built into slopes.
When humans transform a slope into a series of flat surfaces, they form terraces. Crops are then grown on these flat surfaces rather than on the slope, preventing crops from sliding down the slope over time. The image below is of rice paddies grown on terraces.
By building these terraces, water flows down and accumulates in each terrace. If the terraces did not exist, rainfall and water would flow from higher elevations down the hill/mountain, carrying important soil and nutrients with it. Building terraces prevents this from happening.