Most likely Yucca Leaf Spot, a fungal infection spread by water splash. Treatment is ineffective, but you could try spraying with mancozeb, if its still available. Usual course of action is to remove severely affected leaves - this particular infection is more severe on variegated leaved versions of this plant, and worse on Yucca gloriosa, usually. Yucca flaccida varieties rarely seem to suffer from it though.