Proximity refers to the closeness of elements. When a series of elements are positioned sufficiently close together in a composition, our brains deem them to be related as an overall whole - a phenomomen referred to as gestalt. Similar to the way alignment creates relatinships between elements, this forced relationship between them due to proximity creates a kind of unity between the elements, even though they may be different colors, values, weights, shapes, textures, or otherwise unrelated.
Likewise, without the benefit of proximity, visually distinct elements may not seem visually related:
Lastly, proximity is particularly important when used to achieve order and hierarchy, as the above example (on the right) demonstrates. In this example, the shapes have been grouped, the type has been moved closer to these shapes, and finally the title has been increased in weight and size, and moved above the type. These groupings and placements help enforce the hiearchy that the increased weight of the title creates. If I had left the title where it was in the example on the left, the relationship wouldn't have been so immediatly clear.