Think about a tiny portion of a vista, maybe the gleam in a pretty girl’s eye. If this object is a far distance, the light from this tiny object arrives at the lens as parallel rays. The shape of the glass lenses and their density alters the path of this incoming light. It departs the lens as converting rays. A trace of these rays resembles a cone of light. The apex of this cone will form 50mm downstream from the lens (provided the source was at a far distance away (infinity ∞) and the lens has a 50mm focal lenght. Since this 50mm fixed lens has limited ability to alter the angle the rays exit, should the object be closer than ∞, the apex of the cone will form further downstream. When you focus by turning the focus ring on the lens barrel, you are adjusting the distance lens to image sensor / film in an attempt to kiss off the apex of the cone of image forming light on film or sensor.
Briefly, all objects in a vista can be consider to consists of countless tiny points. Each will be the origin of light rays. If the object is distance, these rays enter the lens parallel rays. If the object is close to the camera, the rays striking the lens are not parallel, they are diverging. The lens redirects all these rays. There new path is a cone of light. The apex of the cone of light from each object has a finite length. The shortest distance lens-to-apex is a trace of a distant object. Objects that are close have longer lens-to-apex distances. When you turn the ring, you are adjusting the distance lens-to-image sensor. An object is in focus only when the apex of the cone of the image forming rays kiss the image sensor. When this happens, the object is imaged as a super tiny circle of light. This tiny circle has indistinct margins; we call them circles of confusion. The entire image of a vista consists of countless such circles. Objects in focus reproduce as super tiny circles. Objects out-of-focus reproduces as larger circles. To appear sharp, the circles of confusion must be super tiny, so tiny they are perceived at points of light and not circles of light.
Depth-of-field is that zone before and behind the distance actually focused upon, in which objects appear to be reasonably in sharp focus. This zone contracts and expands based on the diameter of the camera’s aperture setting. Tiny diameters of aperture expand the zone. Depth-of-field has many elements, aperture, subject distance, acuity of the observer’s eye, lighting level of the image being viewed, contrast of the image being viewed, and the distance of the observer to the image being viewed. The complexity of depth-of-field is too great for these few paragraphs. Why not study up on the subject. In a nutshell, if the circles of confusion are seen as points of light, the image will be declared tack sharp. If the circles are visible to the observer as circles and dimensionless points, the observer will declare the image to be fuzzy.
Most depth-of-field tables are based on a circle size of 1/1000 of the focal length. Thus for a 50mm lens, that's 0.05mm. Such a value assumes an 8x10 inch print or image will be made. For 35mm film that requires about 8X magnification. For critical work Kodak used 1/1750 thus 0.028mm.