Carrot seeds come from the flowers of the carrot, and are not found within the carrot itself. The part of the carrot that we eat is in fact the root, and grows under the soil. However, the plant grows "umbels," or groups of flowers above ground that produce seeds.
Carrots grow large stems above ground. These stems produce flowers that grow in groups. Since it takes two years for a carrot to mature, it takes as long for the flowers to produce seeds, which are small and brownish in color. The outer layer of flowers in an umbel mature first, bending outward to expose the seeds when they are ready.