What is the difference between a Solemnity, a Feast and a Memorial on the Church calendar?

Well, it can be a bit confusing. We honor the saints on certain days. There is a difference in ranking, however:

A solemnity is the highest rank of celebration: Easter, Christmas, All Saints Day, the Ascension, Corpus Christi, and other celebrations of events in our Lord’s life on earth and certain saints are solemnities.

In addition, there are particular saints who have Solemnities include the following:
Mary, Mother of God (January 1)
Saint Brigid: (February 1)
Saint David (March 1)
Saint Patrick (March 17)
Saints Peter and Paul (June 29)
Saint Joseph (March 19)
Saint George (April 23)
Saint John the Baptist (June 24)

Feast Days are the second rank. They consist of the celebration of certain saints like the feast of the Archangels or most of the Apostles.

Note: Blesseds do have a liturgical feast day in the universal Catholic Church, but their Feast Day is restricted to local or particular groups.

When a person is beatified by the Pope, the Church grants them the title Blessed and the right to have a liturgical feast day. However, this feast is not celebrated universally across the entire Church. Instead, it is typically granted to specific dioceses or religious orders that have a close connection to the Blessed’s life or work Christianity Stack Exchange+1.

For example:

Blessed Juan Diego had a feast day in the U.S. and Mexico..he has since been declared a Saint..

Blessed Takeri Tekawitha (Lily of the Mohawks) had a feast day in the U.S. and Canada…again, he has since been declared a Saint.

Blessed Stanley Rother has a feast day in the U.S.

These local feast days may include a Mass, Divine Office, and sometimes public veneration (such as images or relics) in those dioceses or orders, but the entire Church does not observe the feast. The feast is a mark of the Church’s approval of the Blessed’s life and witness, but it is not yet the full liturgical veneration reserved for saints.

Key points:

Venerables (those whose heroic virtues have been recognized but not yet beatified) do not have liturgical feast days — public veneration is forbidden until beatification Christianity Stack Exchange+1.

Blesseds can have local feast days, but they are not universal.

Private devotion to a Blessed is always allowed, but public liturgical veneration requires a special permission (indult) from the Holy See.

So, while a Blessed does have a feast day in the Catholic Church, it is local in scope, not a universal feast like that of a saint.

Memorials are the lowest rank and are the celebrations of most of the saints.

Note that these terms are somewhat blurred in many common announcements, especially the latter two. In fact, we have done it ourselves!