The Displace filter (dialogue box below) is only rarely useful. However, studying it can reveal a lot about how the various filters in the Distort submenu works.
In the images below, two files of the same pixel dimensions have been prepared: a face target (left) and a blurry radial pattern source (middle). The filter is run from the target file and after the OK button has been pressed on the filter's dialogue box, PS will ask you to navigate to the source file. The results ((right) are the produce of each pixel in the target being shifted horizontally and vertically according to the black and white values of the source image. If the source image is not blurry then very sudden shifts will result.
This mapped transforming is the basic voodoo that is at the heart of many of the Distort filters and used in the right way the Displace filter can repalce many of its brother and sisters Displace filters. So why use this filter over one of the more 'canned' filters such as Zig Zag filter (which does a reasonable pond ripple)? Well... the complete control over the shape of the distort can obviously be an advantage, but also the information that was used to map the ripple can be re-purposed to light it. The white image below on the left was made by duplicating the source file layer and setting its Blend Mode to Divide. This was inverted and rotated 180 degrees to produce the black image in the middle. The image on the right was made by passing the white pattern over a solid grey in Color Dodge mode and the black layer in Multiply mode.
If the displaced target is substituted for the grey then we have:
In real life one, ripples and suchlike are not as regular as the maps in this demo and such a procedural method for mapping the highlights and shadows is probably not suitable. Painting these things in by hand is a better proposition.