Balarama is the incarnation of Aadishesha, the bed of Lord Vishnu, and has the special presence or avesha of Lord Sankarshana. SriMadhvacharya mentions this in His Bhagavata Tatparya Nirnaya Grantha (आवेशे बलभद्रे). Lord Vishnu has 4 forms known as the Chaturvyuha roopas. These are Vaasudeva, Sankarshana, Pradyumna, and Aniruddha, responsible for providing salvation, cosmic destruction, cosmic creation, and sustenance, respectively. Out of these, Balarama had the special presence of Lord Sankarshana. He incarnated on the earth to serve Lord Krishna in His mission of lowering the burden of the earth by killing the evil people and uplifting the noble people.
While Devaki and Vasudeva were in jail, Kamsa had already killed 6 sons of Devaki. These 6 sons, due to a curse, were born as Devaki’s sons and were killed by Kamsa. That’s why, as Kamsa kept killing these 6 babies, Yogamaya Durgadevi took their souls and kept them in Paatala loka. Now, as per the instructions of Lord Vishnu, Aadishesha entered Vasudeva and then entered Devaki’s womb. Now, after 7 months of pregnancy, Lord Vishnu instructed Yogamaya Durgadevi to transfer this child, which was Aadishesha, from Devaki’s womb to Rohini’s womb.
This was done in order to make sure that the baby was safe along with Rohini, who was a wife of Vasudeva, who was living in NandaGokula along with Nanda Maharaja and his wife Yashoda Devi. This was done because Kamsa had heard in the prophecy that the eighth son of Devaki would kill Kamsa. Now, Vasudeva had 13 wives. Kamsa thought that if the eighth son was born, then it could be possible that Vasudeva, for the sake of saving the eighth child, might exchange it with his wives. So, Kamsa kept Devaki and Vasudeva together and separated Vasudeva from the rest of his wives.
By doing this, Kamsa got clear chances to track the eighth son born to Devaki and Vasudeva, and that would enable him to kill that eighth child, ensuring no possibility of an exchange would take place. That’s why Rohini was staying in NandaGokula. Now, as Yogamaya Durgadevi transferred Aadishesha from Devaki’s womb to Rohini’s womb, the rumor spread that Devaki had a Garbha Paata, which means the baby died in Devaki’s womb itself. But they were unaware of the reality that Yogamaya Durgadevi had performed the transferring of the baby.
Another thing is, this transferring process occurred while Balarama was in Devaki’s womb and not after Balarama’s birth. And due to this, Balarama, the incarnation of Aadishesha, was known as Sankarshana. Whereas, in the case of the Sankarshana form of Lord Vishnu, the meaning is सम्यक् कर्षयति इति सङ्कर्षणः, which means “He who attracts or draws everything together perfectly is called Sankarshana.” Rohini too had performed severe penance to get a child who was very powerful and should be an incarnation of Aadishesha. So, as per her penance, she got Aadishesha himself as her son, in the form of Balarama. Actually, He was named Rama. But since He is powerful, He is known as Balarama.
After that, the unborn Lord Vishnu entered Vasudeva and then entered Devaki’s womb and stayed in the womb for the remaining 3 months and then appeared out of Devaki’s womb in His four-armed form, and was visible to all in the form of Krishna. While He was in the wonderful baby form, Krishna was shining with the radiance of thousands of suns, His eyes like blooming lotuses, holding a conch shell, a discus, a mace, and a lotus in His four hands, wearing a crown, His kaustubha jewel and had a Srivatsa mark on His chest. He was wearing garlands and various ornaments that decorated His body. He was wearing the Peetambara, which was shining like lightning in the sky during rain.
Hope this helps!
Jay SriRam!
ShriKrishnarpanamastu!