One of the requests of Our Lady of Fatima was for Communions to be offered in reparation for the sins of the world on five consecutive first Saturdays of the month. This is still a very good devotion for many reasons, one because it directly helps repair the damage evil has done to the world, and two because it helps us to develop a healthy habit of attending Mass regularly in addition to Sundays.
It also helps promote regularly going to the sacrament of confession, since must be in a state of grace to receive Communion.
In order to complete the devotion, the Rosary should also be said, and we should spend about 15 minutes meditating on Christ or some other holy thing such as one of the mysteries of the rosary. This helps us learn to pray and meditate on Christ’s life regularly.
For more information, this page seems to be pretty good: http://www.themostholyrosary.com/appendix2.htm
You can also consult the Google.