The primary characteristic of transitional fossils is that they exhibit traits from both ancestral and descendant species, providing evidence of evolutionary change. These fossils often display a mix of features that signify the gradual transition between two distinct groups. For example, Archaeopteryx is a famous transitional fossil illustrating the evolution from dinosaurs to birds, showcasing both reptilian and avian characteristics. Transitional fossils are crucial for understanding the evolutionary process and demonstrating how species adapt over time through natural selection.