Many eolian sand grains have well-rounded concavities. These concavities occur in grains of all minerals in a single sample and preferentially at larger grain sizes, suggesting that they form by mechanical abrasion in the eolian environment rather than by chemical dissolution. The concavities develop through abrasion at contacts between near-surface grains in the bed. The energy for this abrasion is provided by collisions of saltating grains with the sand bed. As a grain with a concavity cycles through a range of depths in a ripple, agitation of the bed driven by grain-bed impacts promotes the formation of a grain-grain contact between that concavity and a protuberance on a neighboring grain. This in turn focuses further wear at the contact, thereby circumventing the natural tendency toward grain sphericity that would arise from random grain orientation. A quantitative physical model combining theories of grain-bed impacts and of granular materials with experimental surface erosion rates establishes the plausibility of this mechanism. Within the model, concavities grow to a limiting size that is a significant fraction (order 10-30%) of a grain diameter, within the range of observed concavity sizes.