The idea is that all possible worlds are to be found in one section or another of the diagram. If you let your pointer hover for a moment over an area on the diagram, a caption will pop up telling you what kinds of possible worlds that particular section of the diagram contains. By clicking an area to black, you are eliminating all the possible worlds it contains from consideration - you are saying that the real world or the actual state of affairs isn't one of those possibilities. Try it out - click on the areas within the diagram.
Meaning is exclusion.
You start with an all white table says nothing - it's a tautology, anything's possible. When you click areas to black, by excluding some possibilities, your language becomes more specific and your assertions more meaningful. Euler diagrams and Venn diagrams look identical to one another, and to Johnston diagrams, since all illustrate inclusion and exclusion of one kind or another, but each performs a different task, dividing up different kinds of things. It's possible to think of Euler Diagrams as a special case of Venn Diagrams, and perhaps the same can be said of Johnston Diagrams, but what's being considered is different in each case. Each fulfills it's own pedagogical purpose.