Focus Breathing

Focus Breathing is a phenomenon that causes the focal length of an image to change as the focus setting of the lens is being adjusted. As a product of internal design, a prime lens with a fixed focal length can be prone to breathing just as a zoom lens can be prone to breathing as well. Breathing lenses are considered to be inferior to lenses that are internally designed to not image-shift when the focus is being adjusted. 

Lens Breathing can be a very subtle image shift that may go unnoticed, or in some situations can become a very obvious distraction depending on the viewers perception and whether the scene being captured would serve better to have the image remain unzoomed as focus is changing. 

A Varifocal lens is a lens that by it's design is subject to the focal length changing when the focus is adjusted. 

A Parfocal lens is a lens that has been specifically designed to keep the Focal length fixed as the focus is adjusted.