Mu Cephei is listed in SIMBAD as being a red supergiant rather than a standard carbon star. Visually, this star is bright enough to be seen with the naked eye even from fairly light polluted areas. Observing it with a telescope reveals the striking red color.
Mu Cephei is visible to the naked eye and the distinctive red is noticable even with a moderate telescope. The star has depleted it's hydrogen in it's core and is now fusing helium into carbon, which causes the red coloration.
This star is is one of the largest visible stars. It has been described as a hypergiant. It is a popular and attractive star for visual observations. It is nearing the end of it's life and in it's final moments it may produce a supernova that results in a black hole.
The spectral type is listed as M2-Ia and the star is estimated to be between 1,333 and 2,857 parsecs, a rather wide variation. So it's actual distance to us is somewhat uncertain.