Variety is about varying elements and objects in your image, to avoid making them boring. Variety can also be varying your angles, exposure, composition, etc., to get a few different looks to the same image.
This image below has variety because each shell is completely unique. There is also unity in this image because each shell is still a part of the whole beach. You can vary color, shape, textures, and any other combination of elements.
This image has variety by introducing another element into the foreground of the picture. Without the rocks, this would be just another waterfall image. The rocks add something new, while keeping the same feel in the overall image.
Read about the other Principles of Design.