Parity bonds have the same priority or equal claim on revenues promised to pay debt service.
At any given time, a state or local government may have multiple bond issues outstanding. This stems from the fact a government may issue new bonds for capital projects each year as an example. These bonds may be repaid from the same revenue sources, such as the sales or property tax.
If the issuer does not have enough money to pay debt service on all of its bonds, the issuer may have a classification scheme for which bonds to pay first. Parity bonds have the same priority claim on revenue for debt service in other words, none of the individual bond issues take priority over the others in the order of payment.