Salome was the mother of Zebedee's sons, James and John. She is called by name only in Mark's Gospel and only twice. Salome only appears twice in the bible. She is present at Jesus's crucifixion
Mark 15:40 40. Some women were watching from a distance. Among them were Mary Magdalene, Mary the mother of James the younger and of Joses, and Salome.
Matthew 27:55-56 55. Many women were there, watching from a distance. They had followed Jesus from Galilee to care for his needs. 56. Among them were Mary Magdalene, Mary the mother of James and Joses, and the mother of Zebedee's sons.
John 19:25 25. Near the cross of Jesus stood his mother, his mother's sister, Mary the wife of Clopas, and Mary Magdalene.
This verse from John is used by some to make the case that Salome, the wife of Zebedee, is related to Jesus's mother, sisters or perhaps cousins. This is not conclusive but the argument is compelling.
She accompanies Mary Magdalene and Mary, mother of James the younger on the initial attempt to anoint Jesus's body after his burial.
Mark 16:1 1. When the Sabbath was over, Mary Magdalene, Mary the mother of James, and Salome bought spices so that they might go to anoint Jesus' body.
Luke 24:9-10 9. When they came back from the tomb, they told all these things to the Eleven and to all the others. 10. It was Mary Magdalene, Joanna, Mary the mother of James, and the others with them who told this to the apostles.
Salome is a woman of means. Her husband is a professional fisherman with hired servants. She is one of the people supporting Jesus's ministry. The bible includes her as one of the women who had "followed Jesus from Galilee to care for his needs."
Mark 1:19-20 19. When he had gone a little farther, he saw James son of Zebedee and his brother John in a boat, preparing their nets. 20. Without delay he called them, and they left their father Zebedee in the boat with the hired men and followed him.
Matthew 27:55 55. Many women were there, watching from a distance. They had followed Jesus from Galilee to care for his needs.
Salome clearly believed Jesus to be the Messiah, and whether she had any blood relation to Jesus family or not, this incident involving Zebedee's sons leaving their father to follow the Rabbi indicates Zebedee likely felt Jesus was special, too.
Salome is mostly known for an ambitious request.
Matthew 20:20-28 20. Then the mother of Zebedee's sons came to Jesus with her sons and, kneeling down, asked a favor of him. 21. "What is it you want?" he asked. She said, "Grant that one of these two sons of mine may sit at your right and the other at your left in your kingdom." 22. "You don't know what you are asking," Jesus said to them. "Can you drink the cup I am going to drink?" "We can," they answered. 23. Jesus said to them, "You will indeed drink from my cup, but to sit at my right or left is not for me to grant. These places belong to those for whom they have been prepared by my Father." 24. When the ten heard about this, they were indignant with the two brothers. 25. Jesus called them together and said, "You know that the rulers of the Gentiles lord it over them, and their high officials exercise authority over them. 26. Not so with you. Instead, whoever wants to become great among you must be your servant, 27. and whoever wants to be first must be your slave-- 28. just as the Son of Man did not come to be served, but to serve, and to give his life as a ransom for many."
A mothers pride working overtime. This is an intriguing scene, James and John (along with Peter) were clearly closer to Jesus than the other Apostles. It makes sense that human weakness would take over and the thinking that Jesus was like a worldly king, somebody would make a bid for political position. Jesus humbly points out that positions in God's Kingdom are filled by God and he routes the Apostles' grumblings into a teachable moment by explaining the nature of a servant king.
I also find it intriguing how Jesus alludes to the kind of ending that would befall James and John. John died in exile on Patmos, the only Apostle to not die violently, but James had his head lopped off by Herod. Just like John the Baptist.
If you do a Google image search for biblical Salome, you will get a lot of pictures of a young girl (sometime partially nude) holding some guys head. Sometimes the head is on a platter. The daughter of Herod II (not Herod Antipas) and Herodias is named Salome. She is not named in the bible however, The name comes from Josephus's Jewish Antiquities.
Herodias had divorced Herod II (who was her half-uncle, by the way) and married Herod Antipas while Herod II was still alive. This marriage is what John the Baptist was so vocal about. Having a local religious celebrity publicly shaming her unlawful marriage apparently stuck in her craw, so when Herodias saw how delighted "king" Herod was with her daughter Salome's dancing, she manipulated the execution of said religious celebrity.
This version of Salome clearly sticks with the public more than the mother of Zebedee's sons. I found a couple of images of James and John's mother, but a LOT of images of a hot girl holding some guy's head. Go figure...