In A.D. 325, the Council of Nicaea (see: Council of Nicaea) set aside a special day just to celebrate the Resurrection of Christ. The problem with an official day was deciding whether the Resurrection should be celebrated on a weekday or always on a Sunday as the Christians began remembering the Resurrection every Sunday following its occurrence.
Many felt that the date should continue to be based on the timing of the Resurrection during Passsover. Once Jewish leaders determined the date of Passover each year, Christian leaders could set the date for Easter by figuring three days after Passover. Following this schedule would have meant that Easter would be a different day of the week each year, only falling on a Sunday once in awhile.
Other believed since the Lord rose on a Sunday and this day had been set aside as the Lord's Day, this was the only possible day to celebrate His resurrection. As Christianity drew away from Judaism, some were reluctant to base the Christian celebration on the Jewish calendar.
Finally the Council decided Easter should be celebrated on the Sunday following the first full moon after the vernal equinox. Since the date of the vernal equinox changed from year to year, calculating the proper date can be difficult. This is still the method used to determine Easter today, which is why some years we have Easter earlier than other years.
Since Easter is a celebration of Jesus' Resurrection, you would think there wouldn't be room for paganism. However Easter is one of the holidays most intertwined with pagan symbolism and ritual.
The origin of the word easter isn't certain. The Vernerable Bede, an eighth-century monk and scholar, whose shrine is at Durham Cathedral in NE England, suggested that the word may have come from the Anglo-Saxon Eeostre or Eastre - a Teutonic goddess of spring and fertility. Some recent scholars haven't been able to find any reference to the goddess Bede mentioned and while they consider the theory discredited, others retain it for the time being.