Why does Easter fall on a different date every year?

Because Easter is tied to the Moon as well as to the Sun. In Western churches, Easter is the first Sunday after the "Paschal full moon", a calculated full moon falling on or after 21 March, which stands in for the spring equinox. Since full moons and Sundays drift through the calendar at different rhythms, the result jumps around: Easter can fall on any Sunday from 22 March to 25 April.

The reason for the Moon is history. Christians believe Jesus was crucified at Passover, a Jewish feast set by a lunar calendar, and the church wanted Easter to stay linked to it while no longer depending on the Hebrew calendar. So it built its own lunar arithmetic, called the computus. A key tool is the 19-year cycle: 19 solar years are almost exactly 235 lunar months, so the Moon's phases repeat on nearly the same dates every 19 years.

There is a wonderful side effect. In 525, Dionysius Exiguus, who worked in Rome, published a new Easter table in which he counted years from the Incarnation of Christ. That is where our "AD" years come from.

Today, Catholic and Protestant churches use the Gregorian calendar, while Orthodox churches use the older Julian one, so the same rule usually gives two different Easters.