Easter is unlike other holidays. Independence Day is always on July 4th, Christmas is always December 25th, but Easter’s date changes.
Easter is always celebrated on a Sunday between March 22nd and April 25th, but the exact date moves. The reason for this is quite simple.
The date changes on our modern Gregorian calendar, but not on the Jewish calendar. Easter is always celebrated on the Sunday during the Jewish holiday of Passover. Passover always begins on the 15th day of the month of Nisan. The Jewish calendar, unlike our modern Gregorian calendar, uses the rotation of the moon instead of the Sun to divide the year into months.
According to the Jewish calendar Easter does have a fixed date. It is always celebrated on the first Sunday immediately following the 15th of Nisan or, more specifically, the first Sunday after the Paschal Full Moon. While it may seem to us that Easter’s date changes year to year, it was not so for early Christians.
However, that's not the only unique aspect in dating the celebration of Easter because not all Christians celebrate Easter on the same Sunday. This year the Eastern Orthodox Church will celebrate Easter on April 24th, while Western churches will celebrate it on April 17th. This difference has nothing to do with the moon.
Instead, the answer comes down to our calendars. Western Christians use the Gregorian calendar which has leap days while Eastern Christians use the Julian calendar which does not. Over many years the two calendars have become a bit out of sync. This means that the Orthodox Church can date their Easter on one date while the Western churches use a different date.
In general, the reason why Easter’s date changes each year is due to the original Jewish calendar. We celebrate Easter following the cycle of the Moon instead of the cycle of the Sun. It is only due to our modern calendar that Easter has become a moving holiday.