Lets imagine that you're in a restaurant and the waiter brings the bill to your table. You present your card and he takes it across to the till before returning with the handheld device that lets you put your PIN in. While he was at the till he could have quickly passed your card in front of a hidden video camera, flipping it over so that it recorded the information on both sides.
He then sells all of the information he collects in that way on to others. (The going rate, I understand, is a couple of quid per card). Several months later, someone uses your card details to make expensive online purchases, with you having no knowledge of how they got your details.
The person making those purchases could make those purchases because they'd got the INFORMATION on your card, even though they'd not got the actual CARD.
The NatWest card readers seek to circumvent such fraudulent activity by ensuring that a bank customer making a purchase actually has the card in their possession. Inserting your card into your card reader produces a unique code for that transaction, which is only valid for a few minutes (and only while the card is still in the reader).
Chris