Easter Sunday was on April 22nd in 1962. The date of Easter for any given year is calculated based upon the phase of the moon following the March equinox.
Easter is not a fixed holiday, meaning that it can occur on a range of dates, rather than occurring on a set date every year. The Church determines the date of Easter based upon the March equinox, the day in March on which day and night are closest to equal length. This day is sometimes called the spring or vernal equinox, but that is only true for locations in the northern hemisphere -- in the southern hemisphere, the March equinox occurs in autumn, not spring.
The Church decrees that Easter is the Sunday after the first full moon of the March equinox. If the full moon that year occurs on a Sunday, Easter is set for the Sunday afterward. This prevents Easter from falling directly on Passover.