Many bonds pay interest on a regular basis to their holders. The interest is known as the 'coupon', from the days when bond certificates came with vouchers or coupons attached, which had to be presented in order to receive the interest.
A zero coupon bond, on the other hand, pays no interest. Instead, the bond is issued at a discount to its face or par value. When it is redeemed at maturity, the par value is paid out to the investor. The return to the investor is the difference between the purchase price and the redemption proceeds.
If a USD 100 bond is issued at a 50% discount to face value, and is redeemed ten years later for USD 100, the investor will have made a USD 50 return over that period. That gives very roughly the same return as a 5% coupon - that is, USD 5 a year - though the return is actually rather lower, since the investor has had to wait longer for the payment.
Zero coupon bonds can be traded in the bond market. When they are sold, the price will reflect the time for which they have been held. The redemption price is discounted to reflect the time value of money. Since there is less time to go to redemption than when the bond was issued, the discount factor is lower, so the price will be higher than the issue price (assuming the interest rate is the same).
Many zero coupon bonds are issued by governments. With a corporate zero coupon bond there is always the risk that the company which issued the bond might not be around when the bond matures. However the full backing of the government makes a zero coupon bond good security. US Treasury Bills for instance are zero coupon government bonds which have a short maturity (less than a year).
Other zero coupon bonds are created by financial institutions who buy longer term government bonds and separate the interest payment from the principal. Investors can then buy the 'strip' as a zero coupon bond that is backed by the government's full guarantee. The advantage of strips is that they are typically longer term investments, some up to 20 or 30 years. This makes them appropriate for investors saving for a defined long term purpose, such as a child's college fees, or future retirement.