Medieval priests said the daily Mass at the parish; performed baptisms, weddings and funerals; and sometimes acted as scribes. Once the kings and queens became aware that education played a big part in successfully running a realm, priests were often called upon to do individual tutoring or oversee schools. Since priests themselves were well-educated, they were often in charge of keeping palace accounts and often acted as witnesses on business agreements.
Other obligations included performing Last Rites to the dying, visiting parishioners that were ill, hearing their confessions and bringing them Holy Communion. Priests also made sure that important religious holidays were observed. This went far beyond celebrating Easter and Christmas. Almost every day was dedicated to a Saint. St. Patrick of Ireland, who died in 464, is one of the obvious ones. The priest was responsible for noting the celebration, in this case March 17th, and dedicating a Mass to that Saint.
Priests also got involved in local government and were often appointed as record keepers. This often involved duplicating title deeds and taking care of other legal issues. In a way, medieval priests became the first civil servants, taking care of governmental needs just as their modern counterparts do.
Medieval priests were allowed to marry, but it was still frowned upon. They had to pay a fine and get a special license to do so. If a priest was assigned a parish, that parish was handed down to his eldest son when the priest retired. Plenty of time, and sometimes money, was spent on that son's education so he would be ready for the task.