There are two separate, somewhat incomptaible traditions regarding King Suro.
The first origin story comes from a now-lost work, but is quoted in the Samguk Yusa
삼국유사 (三國遺事) by the 13th century monk Iryeon. This states that a purple rope was spotted hanging from heaven; beneath the rope was a golden box wrapped in red cloth; and inside there were six golden "eggs" that are as round like the sun. Apparently, the next day these eggs "turned" into six boys.
There is no indication of human-like parentage in this origin story - he is simply descended from heaven.
The second parentage comes from the Chosŏn era geography book Sinjeung Donggukyeojiseungram 신증동국여지승람 (東國輿地勝覽). This text names Jeonggyeon Moju the mountain goddess of Mt Gaya, located in the region of the Gaya Confederacy. Traditions has it that, while bathing in a pond, she attracted a divine voyeur: Ibiga, "a heavenly god".
When she opened her eyes, Chonggyon saw the round shadow of the sun falling on the surface of the pond still like a mirror. Something sparkled momentarily. She suddenly felt ashamed. The moment she raised her head and looked up into the sky, her eyes met with the burning eyes of someone along with the sunlinght. At that instant, she cried, "Ah!" and felt the burning sttream of someone's vision penetrating her body. The burning light was none other than that of the sun. Although she tried to hdie her body with her hands in a hurry, it was too late. To be sure, she had already looked Ibiga straight in the face.
Pae-Gang, Hwang. Korean Myths and Folk Legends. Jain Publishing Company, 2006.
And that apparently was enough to get her pregnant. Jeonggyeon Moju is said to have given birth to two boys:
惱窒靑裔. The former is identified as an alternative name for Ijinashi, the founding king of Daegaya, lit. Great Gaya; the latter is said to be King Suro.
Not much else is known about the goddess. However, given her province, it is inferred that she was a kind of patron deity to the people who later made up the Gaya Confederacy. To this day, the Sanshingak shrine on the mountain performs rites every October, praying to her for national prosperity.