What is a Coefficient ring in Ring theory?

In lecture, a (well, actually, two words) word "coefficient ring"-without having been defined-was used in the theorem

Theorem:

If the coefficient ring $D$ is an integral domain then so is its polynomial ring $D[x]$.

What is a coefficient ring? Is a coefficient ring the coefficient of each term in a polynomial ring?

Let $p$ be polynomial in $D[x]$. Then, we can write $p = \sum_n a_nx^n$. We call $a_n$ coefficients of polynomial $p$, and we can say that $D$ is coefficient ring of $D[x]$ since all coefficients are members of ring $D$, and any member of $D$ can be coefficient of a polynomial in $D[x]$.