What is meant by the point-source response of eye or telescope? I have heard  that a source is called unresolved if it is much smaller in angular size than the point-source response of the eye or telescope observing it. What is the meaning of point-source response here?
 A: The point-source response is also called the point-spread function (at least for telescopes). This defines how an idealized dot of light at infinity is imaged by the optics of the telescope (or eye). Instead of appearing as a perfect dot (presumably on a single pixel, assuming sufficiently small pixels, for a camera), the dot is imaged as some complicated pattern due to the optics. For a simple optical system such as a circular aperture (no lenses, mirrors, or anything else, just a hole), the PSF is an Airy disk:

The main mechanism at work here is diffraction through the aperture. For a more complicated optical system, the PSF has more features, though the diffraction pattern due to the aperture is usually one of the dominant ones. Here is the PSF of the Hubble Space Telescope Advanced Camera for Surveys in the F625W filter (the PSF is, unsurprisingly, dependent on which camera is used, and which wavelength):

Notice the scale bar - that's 4 arcseconds, 1 arcsec = $\frac{1}{3600}$ degree, so an ideal point source is spread out into an image of approximately this angular size.
A source is called unresolved if it is smaller than the PSF (in the HST example, smaller than ~4 arcsec) because the image contains very little/no spatial information, despite its perhaps complicated appearance (if there are small enough pixels to adequately sample the PSF, which there should be!). For larger sources, the image on the camera is the convolution of the PSF with the source image. Technically this is still true for point sources, but since the source image is a point, its convolution with the PSF is the PSF, up to a normalization.
