The double headed eagle was an important symbol for the Russian imperial family. It is still used as a national symbol. It is believed that the two heads represent Europe and Asia. One head looks west to Europe, the other east to Asia.
Double headed eagles have been used as symbols for many centuries going back at least to the ancient Hittites. It was used by the Byzantine Empire, which like Russia straddled Europe and Asia.
We saw many examples of this during our trip. The one pictured is at the Peter and Paul Fortress.