Some modern birds will swallow stones, which then reside in their gizzards and aid in digestion of food by helping to grind tough food material. Because birds do not have teeth, they need their gizzards to grind their food, which helps to increase the surface area of the food for easier digestibility. Stones used to help in the mechanical breakdown of food within a digestive tract are called gastroliths ("gastro" = "stomach" and "lith" = "stone") and a colloquial term for gastroliths is "gizzard stones." Apparently dinosaurs also swallowed stones for the same reason as birds; numerous polished stones are associated with some dinosaur remains and are especially convincing when found within the thoracic regions of a skeleton. These stones are typically smooth, polished, and oblate to semispherical.

However, these trace fossils (more so than most other dinosaur trace fossils) are susceptible to secondary reworking by sedimentary processes or could be produced by abiogenic means. Therefore you should be very skeptical of a dinosaurian affiliation for any polished stones from Mesozoic deposits unless they were picked out of the rib cage of a dinosaur skeleton.

These could be gastroliths, or they could be just polished stones. One of the major criteria for suspecting gastroliths in this case is that these specimens were found in Mesozoic rocks that were known to contain dinosaurs. Specimens are in the Museum of Western Colorado's Dinosaur Valley, Grand Junction, Colorado.

Further Reading on Dinosaur Gastroliths:

None that I can find yet - I'll keep looking!

Emory University Dinosaur Trace Fossil Page