Believe - to rely upon, to trust, fully convinced, a self surrendering fellowship, unswerving confidence. Here the word is used to convey they put no confidence in the fact. Implies disobedience to an act previously stated which was having been baptized. There have been those that have objected to this verse because it says the one who does not believe will be condemned not the one who is not baptized. But as we see here in the text and context it is definitely implied by the grammar.
Lets look at the verse first.
Peter has just preached the first sermon and has brought conviction to the hearts of the listeners that it was due to their sin that Jesus was crucified. This would mean that because you have been forgiven of your sins, you should now be baptized out of obedience. Baptism for or towards forgiveness of sins. Baptism for or towards the gift of the Holy spirit. May be traced back to Levitical washings see Lev.