If you come across a marriage record which notes the granting of a dispensation of consanguinity, you should definitely sit up and take note: you are looking at evidence of a common ancestor (or a pair of common ancestors) shared by both bride and groom. However, as Dan MacDonald points out in his Marriage Dispensations in Roman Catholic Marriage Records, the presence of a dispensation does not necessarily imply that a couple were related. It depends on the type of dispensation.
In addition to dispensations of consanguinity and affinity (which indicate a blood or marital relation, respectively, and which are pretty much always of interest to the genealogical researcher), the Church also granted dispensations from certain established rules and procedures surrounding the marriage ceremony.
For example, when John Killeen married Margaret Fahey on 20 December 1852, the priest (Rev. M. Molloy) noted that he had obtained a dispensation from the Bishop of Bytown to perform the marriage ceremony at “a fordidden time.” The “forbidden time” in this case was that of Advent (from the start of Advent to the Feast of the Epiphany); another “forbidden time” would be that of Lent (from Ash Wednesday to Low Sunday, or the first Sunday after Easter).
In 19th-century Ottawa Valley area RC parish registers (and no doubt in the RC registers of many other places too), the most common dispensation was that of a dispensation of one or two (and sometimes, although less frequently, of all three) of the required banns.