Baptismal regeneration is the belief that salvation does not occur until one is baptized. Not only does one have to repent and believe on Christ, but he must also be baptized in water in the likeness of Christ's death and resurrection.
This belief drives from the various verses telling people to be baptized in connection with salvation. The main five examples are:
John 3:5 Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God.
Mark 16:16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Acts 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Acts 22:16 And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord.
1 Peter 3:20b–21 … in the days of Noah, … few, that is, eight souls were saved by water. The like figure whereunto even baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ: