When Jesus and his disciples had gone to the town of Jericho, a blind beggar called out to Jesus. Jesus miraculously cured him of his blindness. As explained in the Gospel of Mark:
Many rebuked him and told him to be quiet, but he shouted all the more, "Son of David, have mercy on me!"
Jesus stopped and said, "Call him."
So they called to the blind man, "Cheer up! On your feet! He's calling you." Throwing his cloak aside, he jumped to his feet and came to Jesus.
"What do you want me to do for you?" Jesus asked him.
The blind man said, "Rabbi, I want to see."
"Go," said Jesus, "your faith has healed you." Immediately he received his sight and followed Jesus along the road.
-Mark 10:46-52, NIV translation.
The phrase "Son of David" was a way to refer to the Messiah who had been promised by the prophets of the Old Testament. The Messiah was to be a descendant of King David who had lived about a thousand years before Jesus. The Gospels of Matthew and Luke say that Jesus was a descendant of King David, in addition to proclaiming that he is the promised Messiah.
Matthew mentions that there was a second blind man who also was healed with Bartimaeus.