You say NO, unspent convictions means someone who has been in trouble with the law and perhaps has Community Service and it is still on going. That would be an unspent conviction, or one that is on your record and may take 6 years to clear. If you have never been in trouble, then you answer no and you have nothing at all to worry about .
Certain criminal convictions will remain on the offender's record forever in the United Kingdom, while other types may be forgiven over time. This system of "unspent" and "spent" criminal convictions was designed to give someone who has committed a minor offence the chance to avoid the problems that arise from having a criminal history. Spent are those that have been removed and unspent are those that are still on record.