The Gestalt Principles refer to the various ways we perceive particular visual elements. These principles are often utilized in document design. Company logos are a great example. Think of any business that's been around for at least a few decades. If you were to look up the original logo, you would likely find something that looks very clunky. In contrast, modern-day logos are often of a sleeker variety, operating on the concept of minimalism.
Take--for instance--the evolution of the Starbucks brand. In less than half a century, Starbucks has managed to come from a colorless, bland logo to a very simple depiction of the classic Starbucks mermaid. While before the image was only a small part of the entire logo, now the logo requires the eye to complete the picture, using the Gestalt Principle of closure. Perhaps you could say that this evolution of the Starbucks logo matches consumer recognition of the brand's trademark icon. In other words, although earlier times when Starbucks was a more obscure cafe required the inclusion of the brand name, nowadays just the abbreviated presence of the famous siren is enough to stir up memories of burnt coffee and non-paying conversationalists.
Figure and Ground refers to our attempts at perceiving depth. Many examples of figure and ground include a simple black-and-white image where the eye will typically either instantly label all black areas as belonging to the background or vice-versa. For instance, the viewer will--at first--see a white vase, and then upon further inspection, the two black silhouettes of faces that border each side will become apparent. Sometimes looking to color differences to determine depth can become confusing.
Similarity describes the tendency to group together all items in an image that look alike. Essentially, we are unconsciously operating under the saying that "if you've seen one, you've seen them all." This is also how camouflage works. A soldier dressed in his battle dress uniform might not look exactly like a tree or a bush, but without further inspection, he is capable of fitting into the scenery.
Proximity/Contiguity refers to the fact that things which are closer together will be seen as belonging together.
Continuity refers to the tendency to continue whatever line we initially saw. For instance, if there are four separate strands that meet together at a single intersection, we will likely see these instead as two lines criss-crossing.
Area is when the smaller item in an image is considered to be the figure (the item in the foreground) while the larger item is considered to be the ground (the background).
If you feel confident that you understand each of these various types of Gestalt Principles, feel free to test yourself. Spokane Falls Community College has a PDF posted on their website with various logos each of which you must label according to the Gestalt Principle utilized.