A dispensation is a granted exception from the rules.
In matters of discipline (not doctrine) a priest, bishop or the
pope can grant a dispensation.
To give some examples:
A priest can grant someone a dispensation to miss mass on a
given Sunday.
A bishop can grant someone a dispensation to marry outside of
the church.
The pope can grant a dispensation allowing someone to be
ordained a priest without first attending seminary school.
This is not to be confused with doctrine. There is no such thing
as a dispensation excusing someone from doctrine.
For instance, the pope can't grant someone a dispensation to
commit adultery. This is because it goes against the Church's
doctrine, and everyone must follow the teachings of Jesus
Christ.