Instead of thinking of a 3D texture as a 3D volume of data, it can be thought of as a 2D texture map that varies as a function of the coordinate value. Since the 3D texture filters in three dimensions, changing the value smoothly blends from one 2D texture image to the next.
An obvious application is animated 2D textures. A 3D texture can animate a sequence of images by using the value as time. Since the images are interpolated, temporal aliasing is reduced.
Another application is generalized billboards. A normal billboard is a 2D texture applied to a polygon that always faces the viewer. Billboards of objects such as trees behave poorly when the viewer views the object from above. A 3D texture billboard can change the textured image as a function of viewer elevation angle, blending a sequence of images between side view and top view, depending on the viewer's position.