Paralogs are two genes which share significant homology within a species. Paralogs are created by gene duplication events and subsequent divergent evolution due to lack of the original selective pressure upon one copy of the duplicated gene. This frees the duplicated copy to acquire new functions under new selective pressures. Compare with orthologs.
The genes encoding myoglobin and hemoglobin are considered to be ancient paralogs. Similiarly, the four known classes of hemoglobins (hemoglobin A, hemoglobin A2 , hemoglobin S , and hemoglobin F) are all paralogs of each other. While each of these genes serve the same basic function of oxygen transport, they have already diverged slightly in function: fetal hemoglobin has a higher affinity to oxygen than adult hemoglobin.
Another example can be found in rodents such as rats and mice. Rodents have a pair of paralogous insulin genes, although it is unclear if any divergence in function has occurred.