The word “Alleluia” comes to us from Hebrew and it means “praise Yahweh.” Traditionally, it has been seen as the chief term of praise of the choirs of angels, as they worship around the throne of God in Heaven. It is, therefore, a term of great joy, and our use of the Alleluia during Mass is a way of participating in the angels’ worship. It is also a reminder that the Kingdom of Heaven is already established on earth, in the form of the Church, and that our participation in Mass is a participation in Heaven. 

During Lent, however, our focus is on the Kingdom coming, not on the Kingdom already having come. The readings in the Masses for Lent and in the Liturgy of the Hours (the official daily prayer of the Catholic Church) focus heavily on the spiritual journey of Old Testament Israel toward the coming of Christ, and the salvation of mankind in His death on Good Friday and His Resurrection on Easter Sunday. 

We Christians today are on a spiritual journey as well, toward the Second Coming of Christ and our future life in Heaven. In order to emphasize the penitential nature of that journey, the Catholic Church, during Lent, removes the Alleluia from the Mass. We no longer sing with the choirs of angels; instead, we acknowledge our sins and practice repentance so that one day we may again have the privilege of worshiping God as the angels do. 

(for more information, please go to catholicism.about.com/od/worship/f/No_Alleluia.htm)