Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere that causes variations of the optical refractive index. The astronomical seeing conditions on a given night at a given location describe how much the Earth's atmosphere perturbs the images of stars as seen through a telescope.
The most common seeing measurement is the diameter (or more correctly the full width at half maximum or FWHM) of the optical intensity across the seeing disc (the point spread function for imaging through the atmosphere). The FWHM of the point spread function (loosely called seeing disc diameter or "seeing") is a reference to the best possible angular resolution which can be achieved by an optical telescope in a long photographic exposure, and corresponds to the FWHM of the fuzzy blob seen when observing a point-like source (such as a star) through the atmosphere. The size of the seeing disc is determined by the astronomical seeing conditions at the time of the observation. The best conditions give a seeing disk diameter of ~0.4 arcseconds and are found at high-altitude observatories on small islands such as Mauna Kea or La Palma.
Seeing is one of the biggest problems for Earth-based astronomy: while large telescopes have theoretically milli-arcsecond resolution, the real image will never be better than the average seeing disc during the observation. This can easily mean a factor of 100 between the potential and practical resolution. Starting in the 1990s, new adaptive optics have been introduced that can help correct for these effects, dramatically improving the resolution of ground based telescopes.
Typical short-exposure negative image of a binary star (Zeta Boötis in this case) as seen through atmospheric seeing. Each star should appear as a single Airy pattern, but the atmosphere causes the images of the two stars to break up into two patterns of speckles (one pattern above left, the other below right). The speckles are a little difficult to make out in this image due to the coarse pixel size on the camera used (see the simulated images below for a clearer example). The speckles move around rapidly, so that each star appears as a single fuzzy blob in long exposure images (called a seeing disc). The telescope used had a diameter of about 7r0 (see definition of r0 below, and example simulated image through a 7r0 telescope).