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Proximity is the distance between elements in a given space.
The principle of proximity not only refers to when (or when not) to group elements together, but to how to group them as well.
Below is an image of a school of fish in which all of the fish are in close proximity.
This close proximity shows that they belong together; they're part of some community. Without providing any background knowledge about either of these species of fish, the image communicates to the viewer that the fish on the left are really unified and organized, in contrast to the purple-pink fish that are scattered around.
Proximity may sound like a really basic idea, but it's an important design principle because the logical arrangement of objects dictates how the viewer perceives a message or idea within the design. Proximity often helps guide the viewer as well.
Look at the simple blue dots below. They are arranged in a fashion that might lead the viewer to perceive them as unified.
Likewise, the image of red dots below might be perceived as orderly.
The image below of green dots might also be perceived as equal or uniform.
However, if you change all the elements around and group them in different places, you suddenly have fragmentation, chaos, or inequality.
A very common example of proximity in action is a business card.
You'll notice in the card above that nothing is grouped together; everything is in its own corner. The viewer is not really sure in what order they should be reading the information. The most logical place to start would probably be in the center; from that point on, you're just supposed to move about the page.
In contrast, when everything is grouped together in closer proximity by elements, there is a logical progression and placement of those elements.
Now the message that's being conveyed on the business card is a lot easier to follow.
Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR MARIO E. HERNANDEZ
