Square ensures that all of your images will have a perfect 1:1 width/height ratio. It does this by adding white bars to expand the image's height or width until it becomes a perfect square. This is especially useful when your product thumbnails and titles are not properly aligning due to different image aspect ratios.
Squaring works especially well for images with a white or transparent background. If your website has a different background color, you can achieve the same thing using the Resize tool to expand the canvas.
Example of Squaring: