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

We honor Jesus and 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.

Those 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.

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!