In most cases, we think of using color management to accurately match colors when moving between different color spaces; ICC profiles are used to describe different color spaces and to make precise transformations to values moved from one to another to maintain consistent appearances. In very rare cases, when profiles are assigned to image files without a color conversion, the appearance of the image changes; values stay the same, but their meaning changes, so the image looks different. So when you use this unorthodox method of color adjustment, you get a change in appearance without changing the values in the file, and this is particularly useful when you want to pay a very small price for making very big changes.
This is worth restating. What exactly is the difference between assigning an ICC profile and using an ICC profile to perform a color conversion? Using an ICC profile to convert color changes values to maintain the appearance of an image. Assigning an ICC profile changes the recipe for colors without changing the values in an image, so its appearance changes.
Real Vs. Abstract Vs. Synthetic Profiles
You could say there are "real" and "abstract" profiles. Real profiles describe the color capacity of real-world devices, like monitors and printers. Abstract profiles describe theoretical color spaces that don’t refer to specific devices, like the standard editing spaces we use in everyday digital imaging—sRGB, Adobe RGB (1998), ProPhoto RGB, etc. Both real and abstract profiles are designed to maintain a consistent color appearance. So what’s a synthetic profile? It’s an ICC profile that’s designed to change color appearance or to solve a color problem.
Creating Synthetic Profiles
You can create synthetic ICC profiles with Photoshop. Go to Edit > Color Settings, and making sure More Options is checked, go to Working Spaces > RGB > Custom RGB. In the final window that appears, you’ll use three variables to create a synthetic profile: Gamma, White Point and Primaries.