An expiration date, also known as an expiry date, is the date when the debit card will run out and not be able to be used again.  After this time there should be a replacement that is sent.  Expiration dates are a form of fraud prevention.

The expiration date can be found on most debit cards, and is usually two figures, the month and the year.  The debit card will usually expire at the end of the month, although with some debit cards it does expire at the beginning of the month which can cause confusion.  It will usually say on the card whether the debit card will expire on the beginning or the end of the month.
When the expiry date is reached the card will no longer be able to be used.  If the card is presented for payment it will be refused and the goods will not be given out.  If the card number is entered to buy something over the internet then the number will be seen as invalid (although some shopping card systems will notice that it is expired).  If the card is used to get money out of an ATM machine then the card will also be refused and it may also be kept by the machine, particularly if the ATM is part of the issuing bank’s network.
The reason why expired cards are not accepted is as mainly as an anti-fraud measure, although there is also an aspect of card maintenance in this as well.  The anti fraud element is because card details can get copied and cloned.  If the card is used immediately then the chances are that this will be spotted and the card will be quickly replaced.  However another tactic has been to keep the card for quite a time and then to start using it when it has been forgotten by the user.  An expiry date stops this.  It also cuts down on cards that are currently being used but not noticed by the card holders.
There is also an element of card maintenance with this.  The cards tend to get old and harder to recognise or be used in machines.  One small aspect of this is that signatures tend to wear out on cards.  Although card holders should replace the cards in this case, many do not as they will lose the use of their cards.  So the card company sends the cards out at the expiry date.