A point-spread function (PSF) is a description of the response of an optical system (such as a telescope) to incoming light from a point, consisting of a mathematical function describing the light-pattern expected on the focal plane. An example would be a function that describes an Airy disk.
There are theories associating specific mathematical functions to particular aperture shapes (e.g., rectangles, slits, circles) and sizes.
PSF subtraction (for point spread function subtraction) is post-processing designed to sharpen images. Airy disks from images of lone stars taken with the same instrument are then used to help sort out the images of the stars with overlapping Airy disks.