Michael,
> This is referring to standard deviation, correct? Additionally, How would you calculate the standard error?
Regarding standard deviation vs. standard error: standard deviation usually refers to the extent of how spread or concentrated the data (or samples) are, while standard error is more used to described the accuracy or reliability of an estimator (e.g., estimated coefficient in a model).
> Why is it an approximation? Because it is derived from a mixed model as opposed to a standard glm?
Yes, the statistics from a linear mixed-effects model are mostly approximate based on asymptotic properties. In other words, they are more accurate if the sample size is reasonably large enough.
Gang