This non-ideal focusing may be caused by aberrations of the imaging optics.
Even in the absence of aberrations, the smallest possible blur circle is the Airy disc caused by diffraction from the optical system's aperture; diffraction is the ultimate limit to the light focusing ability of any optical system.
Instead, the focus is the point from which the light appears to be emanating, after it travels through the lens or reflects from the mirror.
A convex parabolic mirror will reflect a beam of collimated light to make it appear as if it were radiating from the focal point, or conversely, reflect rays directed toward the focus as a collimated beam.
Conversely, it can focus rays directed at the focal point that is behind the mirror towards the focal point that is in front of the mirror as in a Cassegrain telescope.