Here's the definition.
Let $X$ be a Riemann surface and $Y$ be an open subset of $X$. A meromorphic function on $Y$ is a holomorphic function $f\colon Y' \rightarrow \mathbb{C}$ satisfying the following conditions, where $Y'\subset Y$ is a open subset.
(1) Every point $p\in Y - Y'$ is an isolated point.
(2) For every point $p\in Y - Y'$, $\lim_{x\rightarrow p} |f(x)| = \infty$.
The points of $Y - Y'$ are called the poles of $f$.
Then he stated in a remark:
Let $(U, z)$ be a coordinate neighborhood of a pole $p$ of $f$ with $z(p) = 0$. Then $f$ can be expanded in a Laurent series $f = \sum_{n = -k}^{\infty} c_n z^n$ in a neighborhood of $p$.
Why is this so? In other words, why $p$ cannot be an essential singularity?