Witnesses to the marriage were Patrick Donovan and Richard Tobin; and the priest, the Rev. Richard Quinn, noted that a dispensation ‘in quarto & [et] quarto consanguinitas’ (of the fourth to the fourth degree of consanguinity) had been obtained.
both bride and groom were removed by four degrees from a common ancestor
Basically, this indicates that both bride and groom were removed by four degrees from a common ancestor (directly descended from the same 2x great-grandparent, in other words), which would make them third cousins.
Earlier discussion of consanguinity and marital dispensations found here.