n is the energy level (1, 2, 3, etc)
L is the orbital type (s, p, d, f, etc). The value of L starts at 0 and goes up to n-1. So for example, s = 0, p = 1, etc. The s orbital is found in any energy level because 0 is less than 1, 2, 3, etc. The p orbital is found only in energy levels 2 and up because 1 is less than 2, 3, etc but not less than 1. And so forth.
m_L is just a way to describe the # of electron pairs per orbital type. The numbers aren't as important as how many there are. m_L ranges from -L to +L. So for example, with a d orbital, d = 2 and so m_L = -2, -1, 0, +1, +2. Those numbers in themselves don't matter. The point is that there are 5 of them. So there are 5 types of d orbitals, each holding 2 electrons for a total of 10 electrons in the d subshell.
Finally, m_s is the spin. It's either +1/2 or -1/2. In other words, two electrons per orbital type. If you isolate one of the d orbitals of the 5, it will have two electrons. One will have spin +1/2 and the other will have spin -1/2. They spin in opposite directions.
*Note: I wrote L instead of in lower-case to avoid confusing it with the number one. Generally it's written in lower-case.
