Norms for setting this date go back to the Council of Nicaea in 325.
Palm Sunday, similar to Ash Wednesday, is a “movable feast” in the liturgical year that is assigned a date only after the date of Easter Sunday is established. It is always seven days before the celebration of Easter, marking the final Sunday of the Lenten season.
According to the norms established by the Council of Nicaea (325) and later adopted for Western Christianity at the Synod of Whitby, Easter Sunday falls each year on the first Sunday following the first full moon after the vernal equinox. This year the vernal equinox falls on Tuesday, March 20, 2018 and the first full moon after that occurs on Saturday, March 31, 2018.
Therefore, Easter Sunday is celebrated this year on April 1. To calculate Palm Sunday, then, just count backward seven days and you get March 25, 2018.
Besides being the last Sunday of Lent, Palm Sunday is also the beginning of what the Church calls “Holy Week.”
This special week in the liturgical calendar is one where the faithful are asked to slow down and accompany Jesus as he approaches his crucifixion on Good Friday. It is a week where the Gospel passages reflect Jesus’ journey to Jerusalem and his final activities before his death.
There you go. That is why Palm Sunday this year is on March 25.