There are two kinds of "magnitude":
apparent magnitude: the brightness that a star is observed to have
absolute magnitude: the apparent magnitude that a star would have if placed at a distance of 10pc. Absolute magnitude is equivalent to luminosity.
For our purposes we need only understand the following three facts:
1) A difference of 5 magnitudes = a factor of 100 in brightness
2) The scale runs such that brighter stars have smaller magnitudes (i.e., magnitude 1 is 100x brighter than magnitude 6) and magnitudes may even be negative for the very brightest objects.
3) The more distant a star is, the larger its apparent magnitude will be because of the 1/r2 dimming with distance.
Let's try some examples!
1. Star A is of apparent magnitude 15, while star B is of apparent magnitude 10.
a. A is 100 times brighter than B
b. A is 100 times fainter than B
c. A is 100 times less luminous than B
d. A is 5 times fainter than B
e. A is 5 times more luminous than B
2. Star A is of absolute magnitude 15 while star B is of absolute magnitude 10
a. A is 100 times brighter than B
b. A is 100 times fainter than B
c. A is 100 times less luminous than B
d. A is 5 times fainter than B
e. A is 5 times more luminous than B
3. Star A is of absolute magnitude 5. Its apparent magnitude if it were at 10 pc distance would be
a. 100 b. 5 c. not enough information to tell
4. Star A is at a distance of 100pc and its apparent magnitude is 10. Its absolute magnitude is
a. 10 b. 5 c. 100 d. not enough information to tell
5. Star C is of apparent magnitude 2.5, while star D is of apparent magnitude 5
a. C is 100 times brighter than D
b. C is 100 times fainter than D
c. C is 10 times brighter than D
d. C is 10 times fainter than D
e. C has an absolute magnitude of 2.5
6. A star has an absolute magnitude of 3.4. Which of the following is true?
a. if it is 10 pc away, its apparent magnitude will be 3.4
b. if it is 4 pc away, its apparent magnitude will be 4.4
c. if it is 25 pc away, its apparent magnitude will be 2.4
d. its temperature must be known to compute its apparent magnitude
e. there is no relation between absolute and apparent magnitudes