Disclaimer: This question is cross posted in here because the answer might be field dependent.
Let $h: [0, L]\times \mathbb{Z}^1 \to \mathbb{Z}^1$ be a function, called the height function, and lets denote the mean value of $h$ at time $t$ be $\bar h(t)$.
In the paper Anomaly in numerical integrations of the Kardar-Parisi-Zhang equation by Chi-Hang Lam and F. G. Shin, Physical Review E, VOLUME 57, NUMBER 6, June 1998, at page 56, it is given that
$$w := \left < \frac{ 1 \sum_{x=1}^L (h(x,t) - \bar h(t))}{ L} \right >^{1/2},$$
where $L$ is the lattice size used in the numerical integration [...], The brackets denote ensemble averaging, which is equivalent to averaging over time when steady state is being considered.
However, what do they mean by "ensemble average" and "averaging over time" ?