A par bond is a bond that sells at its exact face value. This typically means that a bond sells for $1,000, since this is the face value of most bonds. A par bond will have a yield to the investor that matches the coupon amount attached to the bond.
It is extremely unusually for a bond to trade at its exact face value, since the current market interest rate is always varying, either above or below the interest rate implied by the coupon amount of a bond.
As an example of the differences between market rates and the face value of a bond, ABC International sells bonds having a 6% coupon rate. However, the market interest rate at the time of the bond sale is 7%. Consequently, investors will pay less than the face value of the bond in order to achieve the effective 7% interest rate that they want. If the market interest rate subsequently declines to 4%, then the coupon rate on the bond will look more attractive, and investors will bid up the price of the bond. Thus, a par bond situation is only likely to arise during those brief moments when the market interest rate is exactly aligned with the coupon rate.
Another term for a par bond is to say that a bond is selling at par.