Zero-coupon bonds don't make interest payments. Instead, they are issued at a discount to face value and mature at face value. For example, a bond with a face value of $1000 might be issued at a price of 50 cents on the dollar. The yield is a function of the purchase price, the face value and the time remaining till maturity.
Because zero-coupon bonds provide no cash flow prior to maturity, their duration is equal to their maturity. Coupon-bearing bonds have durations shorter than their maturities. The longer duration of a zero means it has more interest-rate sensitivity than a coupon-bearing bond of the same maturity. It will rise in price faster when interest rates are falling, and fall faster when interest rates are rising.