It shows you squares for a bunch of websites. Those you visited before in that browser are red. By clicking them, you tell the site that they are red, thus that you visited them. Each site belongs to a category and thus it comes to its conclusion.

What do you mean? These red boxes are links to sites you've visited in the past, they aren't showing up in Firefox or Safari because you don't have any of those sites in your browser history.

This works by showing you a grid, each box represents a website, to which the creator has ascribed a category(tech/gaming/etc...)

If you've visited one of those sites the box will appear red, and by clicking on the box you let the site know that it is something you've visited in the past and therefore likely one of your interests.