The absolute magnitude M is the brightness of a star placed at the standard distance of 10 parsecs (32.6 ly). The apparent magnitude m is the magnitude it appears to be viewed from earth. Remember, the bigger the magnitude, the fainter the star. The faintest star that can be seen with the naked eye is about m = 6.5.

Sol
M = 4.83, m = -26.72, distance(ly) = 0.00
Alpha Centauri A
M = 4.38, m = 0.01, distance(ly) = 4.36
Procyon A
M = 2.65, m = 0.37, distance(ly) = 11.44
Sirius A
M = 1.47, m = -1.43, distance(ly) = 8.58

Note all three of those stars are members of multiple systems.

If our Sun were placed more than 70 ly away, we would not be able to see it with the naked eye at all. For the closest star of all, the red dwarf Proxima Centauri(m = 11.05, M = 15.48, dist = 4.24 ly), to be just barely visible to the naked eye, it would have to be moved in to a distance of about half a ly.

For those of you interested in this sort of thing, here’s the math.

m – M = 5log(d) – 5,

where d is the distance in parsecs and logs are to base 10. The quantity (m – M) is called the distance modulus, and contains information as to the star’s luminosity and distance.