The practice of covering the images of Christ and other holy images is uniquely Western. In the current Roman Missal, it is stated that this may take place on the Saturday afternoon before the fifth Sunday of Lent. However, since each local practice may vary, this is not obligatory, and some places may choose to cover the images at a later time in Lent. The coverings are removed typically during the Holy Saturday decoration, in preparation for celebrating the Easter Vigil.
The purpose of covering the holy images is similar to withholding the “Alleluia” from the Church’s liturgies, which is also uniquely Western. The idea is to build anticipation for Easter, while we intensify our desire to come closer to Christ. We first remove the celebratory Easter interjection “Alleluia”, so that we may first focus on mending our ways. We then remove even the images of Christ, so that we may long for seeing Him even more when Easter comes.
I mentioned it is uniquely Western, since the Eastern Catholics and the Orthodox do not have this practice. In fact, instead of removing the “Alleluia”, some of them intensify it. Of course, they would have different ways to intensify their liturgical preparation for and anticipation of Easter; e.g., the reading of “The Ladder” by St. John Climacus.