Why is Easter on a different sunday in March or April every year?  

The First Council of Nicaea established the date of Easter as the first Sunday after the full moon following the vernal equinox. Now is that not simple.
First find out when vernal equinox is.
Second find out when the first full moon is after vernal equinox.
Third find out when the first Sunday after the first full moon after vernal equinox.

I rather wish that the date was a set date each year and did not change as well.

Georgian calendar has not fixed a date for celebration of Easter. The First Council of Nicaea (325) established the date of Easter as the first Sunday after the full moon following the vernal equinox. Equinox takes place on March 21, regardless of the astronomically correct date. The date of Easter therefore varies between March 22 and April 25. Eastern Christianity bases its calculations on the Julian Calendar whose March 21 corresponds, during the twenty-first century, to April 3 in the Gregorian calendar. Therefore, in Gregorian calendar their celebration of Easter therefore varies between April 4 and May 8.

it depends on the moon when the first full moon of the calender year is...