Historically, devotion to the Heart of Mary grew up in parallel, but at a lesser intensity than that of devotion to the Heart of Jesus, only starting to become more prominent during the time of St John Eudes. John Eudes was born in 1601 in Normandy, France. He entered the Congregation of the Oratory of France, founded in 1611 by Cardinal de Berulle and was ordained to the priesthood on December 20, 1625.
St. John brought people to love Christ and the Virgin Mary by speaking tirelessly about their Heart, the sign of the love God shows for us and the communion to which we are called.
To offer them liturgical worship, he composed Masses and Offices in their honor and had the first Feast of the Holy Heart of Mary celebrated on February 8, 1648, at Autun (France,) and the Feast of the Heart of Jesus celebrated on October 20, 1672.
He died on August 19, 1680 and was canonized by Pope Pius XI on May 31, 1925.
Nevertheless, it was not until after the Apparitions at Rue du Bac concerning the "Miraculous Medal" made to Catherine Labouré in 1830, and the establishment of a society dedicated to the Immaculate Heart of Mary, at the Church of Our Lady of Victories in Paris in 1836, that this particular devotion became really well known.
Since then devotion to the Immaculate Heart of Mary, has gradually grown more widespread in the Church, particularly since the apparitions at Fatima.
The main difference between the devotions to the hearts of Jesus and Mary is that the one concerned with Jesus emphasizes his divine heart as being full of love for mankind, but with this love for the most part being ignored or rejected, while devotion to Mary's heart is essentially concerned with the love that her heart has for Jesus, for God.
Therefore, it is not an end in itself, so the love of her heart is meant to be a model for the way we should love God. The fact that her heart is immaculate, that is sinless, means that she is the only fully human person who is able to really love God in the way that he should be loved.
Honoring Mary's Immaculate Heart is really just another way of honoring Mary as the person who was chosen to be the Mother of God, recognizing her extraordinary holiness and the immense love she bestowed on Jesus as his mother, the person who was called to share in and co-operate in his redemptive sufferings.
The aim of the devotion is to unite mankind to God through Mary's heart, and this process involves the ideas of consecration and reparation. A person is consecrated to Mary's Immaculate Heart as a way of being completely devoted to God. This involves a total gift of self, something only ultimately possible with reference to God; but Mary is our intermediary in this process of consecration.
Because of the strong analogy between Jesus and Mary, the consecration to Mary's Immaculate Heart is closely linked to the consecration to Jesus' Sacred Heart, although it is subordinate and dependent on it. That is, although the act of consecration is ultimately addressed to God, it is an act that is made through Mary.