The act of rebaptism occurs when an individual who has been baptized previously is baptized again. This could be due to the individual or his/her church or pastor deciding that the original baptism wasn't valid. Other times the rebaptism occurs as a symbol of rededication to his or her beliefs.
A Biblical account of rebaptism occurred when the apostle Paul found disciples at Ephesus who had only heard of John the Baptist's baptism:
3 So Paul asked, "Then what baptism did you receive?"
"John's baptism," they replied.
4 Paul said, "John's baptism was a baptism of repentance. He told the people to believe in the one coming after him, that is, in Jesus."
5 On hearing this, they were baptized into the name of the Lord Jesus.
Various Church Views
After Brigham Young had led the Mormons to present day Utah in 1856, the members of the sect were rebaptized to show their rededication to Mormon ideals. Today Mormons still practice rebaptism, but only for previously excommunicated members to rejoin the church.
In the Eastern Orthodox Church rebaptism is not required as long as the candidate was originally baptized in the name of the Trinity.
In Baptist tradition rebaptism is usually prescribed if the mode of baptism was anything else other than immersion.
The Church of Christ usually doesn't accept baptism of other denominations, so rebaptism is usually prescribed for new converts. The is usually because of the mode of the original baptism (sprinkling or pouring) or reason for baptism was judged to be for unbiblical reasons.