Have you ever made purchases over the phone or online and the merchants asked for the three-digit security code on the back of your credit or debit card?
This is to verify that the card definitely is in your possession. It's information that wouldn't be available to someone who has intercepted your card number and expiration date.
That said, it's important to make sure you know to whom you're giving this information over the phone or on websites.
Con artists often are able to obtain partial information about a potential victim's account, and then contact the person masquerading as a company representative to "verify" the account by requesting additional details such as the three-digit security code. But they might just as well ask for other pertinent details--for example, they may provide the last four digits of your account number (which typically show up on sales receipts) and request the other 12 digits to "confirm" it. Or they already may be in possession of your full account number and request the expiration date of the card, or your billing address. Any of these individual bits of information may be just what the scammer needs to "fill in the blanks" and gain full access to your account, so beware.
Keep in mind, though, that legitimate businesses or financial institutions may request your three-digit security number (called Card Validation Code or "CVC2" by MasterCard and Card Verification Value 2 or CVV2" by Visa) to authenticate a transaction. Again, just be sure you know whom you're talking to before giving it out.