The heart has always been seen as the "centre" or essence a person ("the heart of the matter," "you are my heart," "take it to heart," etc.) and the wellspring of our emotional lives and love ("you break my heart," "my heart sings," etc.) Devotion to the Sacred Heart of Jesus is devotion to Jesus Christ Himself, but in the particular ways of meditating on his interior life and on His threefold love -- His divine love, His burning love that fed His human will, and His sensible love that affects His interior life.
Pope Pius XII of blessed memory writes on this topic in his 1956 encyclical, Haurietis Aquas (On Devotion To The Sacred Heart).
The Friday that follows the Second Sunday in Time After Pentecost is the Feast of the Sacred Heart which brings to mind all the attributes of His Divine Heart mentioned above. Many Catholics prepare for this Feast by beginning a Novena to the Sacred Heart on the Feast of Corpus Christi, which is the Thursday of the week before. On the Feast of the Sacred Heart itself, we can gain a plenary indulgence by making an Act of Reparation to the Sacred Heart.
From the earliest days of the Church, "Christ's open side and the mystery of blood and water were meditated upon, and the Church was beheld issuing from the side of Jesus, as Eve came forth from the side of Adam. It is in the eleventh and twelfth centuries that we find the first unmistakable indications of devotion to the Sacred Heart. Through the wound in the side, the wound in the Heart was gradually reached, and the wound in the Heart symbolized the wound of love." (Catholic Encyclopedia)
This general devotion arose first in Benedictine and Cistercian monasteries of that time, especially in response to the devotion of St. Gertrude the Great, but specific devotions became popularized when St. Margaret Mary Alacoque (1647-1690), a Visitation nun, had a personal revelation involving a series of visions of Christ as she prayed before the Blessed Sacrament. She wrote, "He disclosed to me the marvels of his Love and the inexplicable secrets of his Sacred Heart." Christ emphasized to her His love -- and His woundedness caused by Man's indifference to this love.
He promised that, in response to those who consecrate themselves and make reparations to His Sacred Heart, that:
HISTORY OF THE FEAST OF THE SACRED HEART
The first feast of the Sacred Heart was celebrated on August 31, 1670, in Rennes, France, through the efforts of Fr. Jean Eudes (1602-1680). From Rennes, the devotion spread, but it took the visions of St. Margaret Mary Alacoque (1647-1690) for the devotion to become universal.
In all of these visions, in which Jesus appeared to St. Margaret Mary, the Sacred Heart of Jesus played a central role. The "great apparition," which took place on June 16, 1675, during the octave of the Feast of Corpus Christi, is the source of the modern Feast of the Sacred Heart. In that vision, Christ asked St. Margaret Mary to request that the Feast of the Sacred Heart be celebrated on the Friday after the octave (or eighth day) of the Feast of Corpus Christi, in reparation for the ingratitude of men for the sacrifice that Christ had made for them.
The Sacred Heart of Jesus represents not simply His physical heart but His love for all mankind.
The devotion became quite popular after St. Margaret Mary's death in 1690, but, because the Church initially had doubts about the validity of St. Margaret Mary's visions, it wasn't until 1765 that the feast was celebrated officially in France.
Almost 100 years later, in 1856, Pope Pius IX, at the request of the French bishops, extended the feast to the universal Church. It is celebrated on the day requested by our Lord-the Friday after the octave of Corpus Christi, or 19 days after Pentecost Sunday.