For observations from the Earth's surface, turbulence in the Earth's atmosphere causes point sources (such as stars) to be smeared out and twinkle. This is known as seeing. Under the best atmospheric conditions, point sources will be smeared out to an angular diameter of about 0.5".
The trigonometric parallax of an object at a distance of 1 parsec is 1", however, there are no known stars beyond the Solar System with parallaxes greater than 1". The nearest star to the Sun, Alpha Centauri (actually a triple star system), is about 1.3 parsec away with a parallax of 0.75".