In my logic class we started learning about the different complexity classes. In particular, we focused on the NP complexity class. A problem is in NP if it is solvable in polynomial time using a nondeterministic Turing machine. To show that a problem $L$ is NP-compelete, we have to show that: $1)$ $L$ is in NP, and $2)$ if $L$ is solvable in polynomial time, then all problems in NP can be solved in polynomial time.
In regards to $2)$ we can use reduction. So if you already know a NP-complete problem $M$, then it is enough to show that we can use a polynomial time algorithm that we can use for $L$, in order to solve $M$ in polynomial time.
I'm not sure I understand the explanation for the reduction section.