The age of a coin is the time since the coins were last used or held. This is a different approach from the usual form of PoS where mining is made easier for users who have the highest stake in the altcoin. In the coin-age-based approach, the age of the coin (coinage) is reset every time a block is mined. The miner is rewarded for holding and not spending coins for a period of time. This mechanism has been implemented in Peercoin combined with PoW in a creative way.
The difficulty of mining puzzles (PoW) is inversely proportional to the coinage, meaning that if miners consume some coinage using coin-stake transactions, then the PoW requirements are relieved.