In the case of the Bible it indicates the presence God.
The early church told the miracle stories to one another to remind themselves of the signs that Jesus had shown them while he was still with them. This would in turn give them hope of better days to come. The early church was also being persecuted at the time, so telling the miracle stories reminded them that through the miracles they could defeat their enemies and spread the word as Christ had promised.
There are four main different types of miracles that are shown in the gospels are. the signs of the kingdom, healing miracles, exorcisms and nature miracles. The sign of the kingdom is depicted in the life of Jesus Christ, who is the son of god born to humanity and lived like any other human. By coming to the humanity, Christ shows the presence of the kingdom of God. His resurrection and ascension also depicts the presence of the kingdom. Healing miracles are shown when Jesus heals the sick and raises the death for instance the story of Lazarus and many others who were healed. Exorcisms are miracles shown when Jesus drives away evil spirits that possess people, for instance, the evil spirit that was expelled into swines. Nature miracles are shown in the book of Matthew when Jesus rebuked a storm and it stopped just from the words spoken by Jesus.
In the book of Luke chapter 8 from verse 41, there are the miracles of raising Jairus daughter and the healing of the woman with hemorrhage. As Jesus was coming Jairus came to him with information that his child was sick and asked him to accompany him to his house to heal the girl. As they were going the crowds were pressing on him and the woman with hemorrhage came and touched his cloth, and he felt power go away.