Definitions for "Soft proof"
a proof that you would receive over the internet, such as a PDF file
a representation of your image on your monitor
Soft proofing is previewing, on a monitor, how an image's colors (or shades of gray if a black and white image) will look when reproduced by another device, such as a printer. To soft proof in Photoshop, Photoshop must have access to the profile the targeted device will use to process the image. For more about soft proofing, click here.