Consecutional means that Saving Faith is the Consequence of Saving Grace. For The New Light Calvinist, this also means Saving Repentance and Saving Faith are the result of regeneration and the indwelling of the Holy Spirit. "For by grace are ye saved through faith; and that not of yourselves: it is the gift of God". Saving grace is the cause of saving faith... anything other than consecutional faith is not saving faith.
For a complete explanation of the basis of the New Light Calvinist decision for Christ, please read Samuel Hopkins.