How many electrons can have the quantum number set n=5, l=3, ml=-1? How many electrons can have the quantum number set $n=6,\ l=3,\ m_l=-1$?

Also, please explain why. I know that n describes the number of shells in an atom but what do n, l, and ml have to do with electrons?
This post answers the question of the of what the other quantum numbers mean:

What do the quantum numbers actually signify? 

As for how many electrons can have $n=5,\ l=3,\ m_l=-1$...

The Pauli Exclusion Principle states that two identical fermions (an eletron is a type of fermion) cannot occupy the same quantum state. 


  In other words, two electrons (in the same atom) cannot have identical quantum numbers.



For each $n$, the values of $l=0,1,2,...,n$
For each $l$, the values of $m_l=-l,...,-1,0,+1,...,+l$


For each $m_l$ there are only two allowed values of $m_s$, namely $m_s = + \frac{1}{2}$ and $m_s = -\frac{1}{2}$. Thus, each set of $\{n,l,m_l\}$ can only describe two electrons. In your case, we have two electrons with $n=5,\ l=3,\ m_l=-1$:


$\{n,l,m_l,m_s\}=\{5,3,-1,+\frac{1}{2}\}$
$\{n,l,m_l,m_s\}=\{5,3,-1,-\frac{1}{2}\}$