The name Jairus in the Bible
There's only one man named Jairus in the Bible. He is the temple official who comes up to Jesus, pleading for his twelve year old daughter's life (Mark 5:22, Luke 8:41). When Jesus begins to follow him to his house, a woman stops them. She has been sick for as long as Jairus' daughter has lived, and during that time doctors have winged her out of her money without curing her. She heals spontaneously when she touches Jesus' garments, and Jesus and she enter a brief conversation. While this is going on, Jairus' daughter passes away.
Jesus and Jairus, and Peter, James and John enter Jairus' house and find people loudly wailing. But when Jesus says that the child is only sleeping, they suddenly aren't too sad to laugh. Jesus forces them out, takes Jairus and his wife to the girl's room, and tells her, "Talitha kum." And she awakes.
Etymology of the name Jairus
The name Jair—and thus the name Jairus—comes from the root verb אור ('or), meaning to be light or to shine:
For a meaning of the name Jair, BDB Theological Dictionary suggests One Giving Light or He Enlightens. Jones' Dictionary of Old Testament Proper Names reads He Will Diffuse Light or He Will Enlighten. Spiros Zodhiates (The Complete Word Study Dictionary—New Testament), says that the name Jairus means Jehovah Enlightens, but technically the name YHWH (or Jehovah) is not contained by this name.