Unlike most of the world that celebrates Corpus Christi (latin for "Body of Christ") on Thursday because the Eucharist was instituted on Holy Thursday, the United States of America celebrates it on the following Sunday. While many traditional parishes (that will say the Traditional Latin Mass) will still celebrate Corpus Christi on the Thursday after Pentecost, all parishes (even traditional ones) have permissions to transfer its celebration to the subsequent Sunday (i.e. 1st Sunday after Pentecost). This indult to the United States was granted by His Holiness Pope Leo XIII.
Corpus Christi is now called in the Post Conciliar Church (i.e. after Vatican II) the Solemnity of the Body and Blood of Christ. We remember and again celebrate this true and lasting miracle. Think about it, we can receive the flesh and blood of Our God! We can truly receive our Creator in a way so that we might have life within us! The Institution of the Eucharist changed the world. We must contemplate this miracle before receiving Our Lord at every single Mass. How can we not share the sentiments of Archbishop Sheen who said, "The greatest love story of all time is contained in a tiny, white Host."
Around the early 1200s, Saint Juliana of Mont Cornillon received a vision concerning this feast at a young age. St. Juliana always had a strong devotion to the Blessed Sacrament. In her visition she saw the Church under the appearance of the full moon. One large, dark spot was in the moon - symbolic of the absence of a solemnity to honor the Holy Eucharist. St. Juliana became an Augustinian nun in Liége, France, in 1206. Corpus Christi became a feast for the Diocese of Liege in 1246, and later in 1312, Corpus Christi became a mandatory feast in the Roman Catholic Church. In 1970 the name was changed from Corpus Christi to the Solemnity of the Body and Blood of Christ when Corpus Christi and the Feast of the Precious Blood (July 1) were joined. Traditional Latin Masses still separately celebrate the Feasts of Corpus Christi and the Feast of the Precious Blood.
Today's feast has 3 purposes:
1) To honor Our Lord, who is truly present in the Holy Eucharist
2) To instruct others on the faith, mystery, and devotion concerning the Holy Eucharist
3) To show our appreciate for the great gift of the Holy Eucharist
Many parishes will have Eucharistic processions. These processions are endowed with indulgences by Popes Martin V and Eugene IV.