The Shrouded Cross is draped with a burial cloth to signify the message of the crucifix, Christ's resurrection, and the hope of new life for believers.
It is also known as a Draped Cross.
In most traditions, the sanctuary cross is draped in color during Lent (purple), Good Friday (black), and Easter (white). Some churches leave white on the cross through Eastertide, drape the cross in red for Pentecost Sunday, and then leave the cross undraped until the beginning of Lent the next year.
Red being the color of blood, symbolizes martyrdom. It is also an alternative color for the last week of Lent, called Holy Week, which begins with Palm Sunday.
Red is the color for Pentecost Sunday and for ordinations and installations, because it is the color of fire and therefore also of the Holy Spirit (see Acts 2:3).