It is a log scale in intensity. Thus, magnitude and intensity both are scales for brightness of a star. Specifically, if star A is 100 times brighter than star B, then the difference between the magnitudes of A and B is defined to be 5.
mB - mA = 5 .
Note that a dimmer star has a larger magnitude number. We arbitrarily choose one fixed star as the reference and define its magnitude as zero. Then, the magnitude one stars are about 2.51 times dimmer for 2.515=100. Similarly, a magnitude 5 star is 100 times dimmer. The relation between the intensity, I and magnitude, m is
m = - 5/2 log 10 ( I / I 0) .
(What is I0?) The following figure shows the magnitudes of some common objects.