Equal rights are the rights here being talked about is related to the right over the coupon. At the time when the coupon is being paid, the parity bonds will have the equal rights as already issued bonds. So in case the bonds already issued are unsecured bonds with coupon rate 5% and new unsecured bonds issued are at 10% then they have equal rights over the coupon. Secured bonds will always have an over and above rights over the unsecured bonds.
Bond is a financial instrument which is issued by the financial intermediaries in order to raise funds. A bond is generally issued with a coupon rate. A coupon rate is the rate at which interest or coupon absolute amount will be paid to the buyer of the bond. The coupon rate will be paid annually or semi-annually depending on the type of issue. Different type of bonds are issued by changing there year of maturity, coupon rate or the type i.e. secured or unsecured bonds.