What is the cause of all of these sharp, concentric rings around bright stars in this HST image?
The diffraction pattern at the focal plane created by a circular aperture is called an Airy Disk or Airy Pattern.  Both the outer opening and the inner hole plus secondary contribute to the exact function.  This is usually not easily observed with ground based telescopes because the seeing fluctuations due to air turbulence smears it out.  These images use filters that are a few 100 Angstroms wide, so although not monochromatic, they are narrow enough to clearly see the pattern.  The spectral shape of the star's light within the filter makes the effective width of frequencies more narrow.