Structure: The parameters for placement of information, ideally aiding in information comprehension.
Organization: Organization is the use of space, both positive and negative, to place information in ways that are most beneficial to information comprehension. The act of structuring.
Hierarchy: The act of classifying a group of things so that the most important things are kept together in one place and the last important things are kept in another. In information design, typically the most important information comes first, with less necessary information coming later.
Visual Grammar: The use of proper markings in visual design, especially concerning those markings that have been added since computers have come around and can be hard to distinguish between.
Bad example: I eat EVERYTHING!
This is a very bad example of form design. The organization and structure is poor because the drop down box says "I eat everything" and then directly below is a check box section that lists animals. The header for the check box section simply reads "animals" it doesn't say "animals you own" or anything of that matter, and so it makes it look like it's asking about which animals you eat.
Some extra white space between the two, or just a better header would help stop the confusion.