Concrete has tremendous strength in compression , very little comparatively in tension . If the dam is designed with a convex curve on the reservoir side , water pressure tends to create compression in the concrete . You can demonstrate this by bowing a playing card in one hand , so the side toward your finger tips is bowed in that direction . If you apply pressure to the card on the convex side you will feel a slight increase of outward pressure from the ends of the card . Conversely , putting a little pressure on the concave side will increase the bowing and reduce the end pressure .
Thus water pressure on the reservoir side tries to push outward on the hillsides at each end , anchoring the dam more stongly , while increasing the compressive stress in the concrete . Properly designed the entire concrete structure will be in compression when the reservoir is full . The Hoover/Boulder Dam holding back Lake Mead is a good example . The dam gets stronger as the lake level increases due to increased compressive loading .
A straight dam tends to bow to the downstream side , increasing the tensile stress on that side , which could result in total dam failure , plus reducing the outward pressure anchoring the dam to the hillsides on both ends .
BUT ! A properly designed bowed dam requires more concrete due to the longer length !