The veiling of statues is an option given in the roman Missal of a tradition starting before the 13th century. By veiling these images, we recognize the last two weeks of lent as a special time to mourn Jesus' passion, death, and time in the tomb until the joy of Easter Sunday.
What the USCCB has to say
"the Catholic Church recommends this practice to heighten our senses and build within us a longing for Easter Sunday."
"Through this absence of images, our senses are heightened and we become more aware of what is missing."
"Christ veiled his divinity during his passion."
"The custom of veiling the images during the last two weeks of Lent hails from the former liturgical calendar in which the Passion was read on the Fifth Sunday of Lent (hence called "Passion Sunday") as well as on Palm Sunday, Tuesday and Wednesday of Holy Week, and Good Friday."