When you manually adjust your focus ring on the lens, what actually happens inside the lens? Is this changing simply the point at which the lens is focusing, so that anything at this distance away from the camera, within some tolerance, will be in focus? How does this work?
Yes, the manual focus mode on lenses lets you manually change the point of focus. Actually what you're setting is the plane of focus, an entire plane, perpendicular to the optical axis, where the image is in focus.
The distance to the plane of focus is not constant, though - the larger the angle from the optical axis, the longer light has to travel to get to the camera from the plane of focus.
The "tolerance" you're referring to is called the depth of field which is the distance between the closest and furthest objects in an image that appear acceptably sharp.
What physically is going on in the lens is that by turning the ficus ring, is that lens elements within the lens move towards the front or back of the lens, changing the plane of focus. That the plane of focus does change when moving the lens elements is a result of optics.