Gestalt principals have to do with what is known as "visual perception." It's how people view visual information and organize what they see. Gestalt, in German, means form or shape. By nature of the eNotes answering system I can't draw examples for you, but I'll try to describe them or provide links.
Similarity is the idea that our mind will put together separate shapes into a bigger picture as long as the shapes are similar. For example, you may make a circle out of 22 different pie shaped wedges that are slightly separated. Your mind will put them together so that your eye perceives the circle rather than 22 separate items (though, of course, if you are looking for 22 separate items you will see them as such.) Here's and example.
Proximity goes along with similarity. The items really have to be close together for the trick to work. If the pie-wedges were pulled too far apart your mind would not bind them together. In essence, it's saying the similarity isn't enough...the shapes must be close together as well. How close depends on the number of shapes, the complexity of the design, and the distance from viewing.
Closure is another interesting one. If you draw a circle that is only 3/4 finished a person will still see it as a circle. The mind will fill in the missing bits. Again, how much can be missing depends a lot on the complexity of the design. Closure occurs when a viewer is able to "close the shape" with his/her mind and see the picture for what it is. A failure of closure would lead to misperception. Here's an example.
All of these apply to the overriding concept of simplicity. Basically, this says that the mind will try to turn visual chaos into something simple. You may look up in the sky and see a bunch of crazy clouds, but given a second your mind will start to put them in simple shapes. Look at a tree and your mind will see the overall shape of the canopy, not the millions of individual shapes the leaves make up. The whole of the shape is more important to our perception than the sum of all the little parts.