Bonds are financial instruments that provide buyers with a fixed return that is a percentage of the face value of the bond irrespective of the actual price of the bond. When interest rates rise, the price of bonds falls.
To analyze with this happens let the price of a bond be P and the interest that a person who buys the bond receives be I, which is a percentage of the face value. The rate of return that is offered is equal to I/P. If there is a rise in interest rates of r, the discounted rate of return is (I/P)/(1 + r). To maintain the same required rate of return, the price P has to drop as I does not change.
The price of bonds falls when interest rates rise to accommodate the discounted returns.