Psi Capricorni, as implied by the name, is located in the constellation Capricornus, which most people will probably know as Capricorn from the zodiac. This is actually a very nearby star at a distance of only 46.3 light years (or 14.2 pc) [1,2], which means that TV viewers in the star system would currently be watching "Kojak", "Are You Being Served?", and "MASH". The star has a stellar classification of F5V [3], which means that it is slightly warmer than but otherwise similar to the Sun.
As seen from Earth, the star has a apparent magnitude of 4.1 [4]. For reference, the brightest stars in the sky have a magnitude of about 0, and the faintest stars visible without a telescope have magnitudes of about 5 or 6, so Psi Capricorni is actually visible to the naked eye. If you actually want to go look for it, first imagine that Capricornus is a warped triangle of third and fourth magnitude stars with one corner pointing south. Psi Capricorni is just northwest of the southern point of that triange. To be honest, I have never identified the constellation Capricornus in the sky, so I would definitely have trouble finding this specific star.
One of the distinct characteristics of Psi Capricorni is that it is rotating very fast for a star. Just like all planets rotate, all stars also rotate. The Sun rotates at a speed of about 2 km/s (or 7200 km/h) at its equator [5]. Psi Capricorni is rotating at a velocity of 42 km/s (or 151,200 km/h) [6]. These sound like really fast velocities, but when you consider that the Earth is orbiting the Sun at a velocity of about 30 km/s (or 108,000 km/h), it doesn't seem too extreme. Still, Psi Capricorni is rotating extremely fast for a Sun-like star.
What makes Psi Capricornus interesting is not that it is rotating very fast but that it was the first star other than the Sun in which differential rotation was observed. Even though the Sun and other stars are rotating, they are also giant balls of ionized gas, so stars do not rotate like solid planets like the Earth. Instead, the areas near the equator and near the poles rotate at different velocities. With the Sun, it is possible to measure this differential rotation by watching sunspots travel across the face of the Sun; the measurements show that the rotation period near the equator is 25 Earth days and near the pole is about 31 Earth days [5].
The tricky thing with stars is that it is incredibly difficult to make images that show any details of the stars' surfaces unless they are exceptionally large stars to begin with. Like I indicated in the introduction, Psi Capricorni is not that different from the Sun, so it's not exceptionally large, and even though it is very close to the Earth, it is not that close. So, to measure differential rotation around Psi Capricornus, Ansgar Reiners and Jurgen H. M. M. Schmidtt at the University of Hamburg along with Martin Kurster at the European Southern Observatory performed careful spectroscopic observations of the star in the year 2000. They specifically focused on measuring the Doppler shifting of iron and silicon in the atmosphere of the star, which creates dark lines in the star's spectrum. When the brightness of the star is plotted versus wavelength, the shape of these absorption lines on very small scales are more consistent with differential rotation in Psi Capricorni instead of Psi Capricorni rotating like a single solid object [6]. Interestingly, the ratio of the rotation period near the equator to the rotation period near the poles is the same for both Psi Capricorni and the Sun, although this was probably just a cool coincidence.
When this research was published in 2001, this was, as far as either the astronomers or I know, the first time that anyone had been able to measure differential rotation in a star other than the Sun. While multiple other differential rotation measurements have been made since 2001, Psi Capricorni will always stand out as one of the first stars where such measurements were made.