Club Validity refers to the time for which your current club status remains active. Once a player accumulates enough culture points his club status is upgraded immediately.
For example, if a Diamond Club player accumulates 1400 Culture Points on 5 July, he is upgraded to Platinum Club on that very day. His Platinum Club status will remain valid till 31-October i.e. 3 months in addition to upgrade month. Upgrade month is the month in which a player upgrades to the higher club.