Divine Mercy Sunday is one of the newer feasts on the Roman Catholic Church's liturgical calendar. Established on April 30, 2000, when Pope John Paul II canonized St. Maria Faustina Kowalska of the Most Blessed Sacrament, Divine Mercy Sunday is celebrated on the Octave of Easter, the Sunday after Easter Sunday.
There are a number of devotions associated with Divine Mercy Sunday, and some, including the Divine Mercy Novena and the Divine Mercy Chaplet, can be practiced throughout the year. The chaplet, in particular, makes an excellent daily devotion, especially if it can be recited at 3 P.M.--the time of Our Lord's Passion and Death on the Cross.
Two devotions, however, can only be performed on Divine Mercy Sunday, because they have indulgences attached to them--one partial and one plenary. You can learn more about those devotions, and the conditions that must be fulfilled in order to receive the indulgences, in Divine Mercy Devotions.