A monic polynomial is a polynomial with a leading coefficient of 1. That is, if $P_n(x)$ is a polynomial of degree $n$ in the variable $x$ then the coefficient of $x^n$ in $P_n(x)$ is 1.

For example, $x^5+3x^3-10x^2+1$ is a monic 5th-degree polynomial. $3x^2+2z-5$ is a 2nd-degree polynomial which is not monic.