The depressor labii inferioris muscle helps to depress and everts the lower lip. It is the most important of the muscles of the lower lip for this function. It is an antagonist of the orbicularis oris muscle. It is needed to expose the mandibular teeth during smiling.
The depressor labii inferioris muscle has also been called the quadratus labii inferioris muscle. Note that in the 1918 edition of Gray's Anatomy illustration used here that its abbreviation is "Quad. labii inf.".