Sankarshana is one of the names of Balarama. Balarama is an avatar of Vishnu for some communities in Hindu religion. Others believe that he is an avatar of Adi Sesha. But the story as to why Balaram is known as Sankarshana is the same in all scriptures.
Six children of Devaki were mercilessly killed by Kamsa as a voice from sky had stated that Kamsa will be killed by the eighth child of Devaki and Vasudeva. She conceived the seventh child in the prison of Kamsa. In the seventh month of her pregnancy the fetus was transferred, with the blessing of Bhagvan Vishnu, to the womb of Rohini, first wife of Vasudeva who lived in Gokul.
The child was born in due time at Gokula.
As the fetus was transferred from one womb to another the child born was also known as Sankarshana. Sankarsha means to transfer.