In semi-arid areas, multiple equilibrium states of an ecosystem (e.g., grassland and desert) are found to coexist, and the transition from grassland to desert is often abrupt at the boundary. A simple ecosystem model is developed to provide the biophysical explanation of this phenomenon. The model has three variables: living biomass, wilted biomass, and soil wetness. The moisture index, which is the ratio of the annual precipitation to potential evaporation, is the only external climate driving force, and the key mechanism is the vegetation-soil interaction. It is found that the maintenance of a grassland requires a minimum moisture index, and the abrupt transition occurs when the moisture index is around this critical value. These results are robust within a wide range for most model parameters, suggesting that the model may be applicable to other temperate grasslands. The characteristics of the wilted biomass also strongly influence the ecosystem's dynamics.