I was reading the Wikipedia article on Robust Statistics: http://en.wikipedia.org/wiki/Robust_statistics#Properties_of_M-estimators
What is meant by the distribution of an estimator, as used here,
It can be shown that M-estimators are asymptotically normally
distributed, so that as long as their standard errors can be computed,
an approximate approach to inference is available. Since M-estimators
are normal only asymptotically, for small sample sizes it might be
appropriate to use an alternative approach to inference, such as the
bootstrap.
Best Answer
Following Henry and Gung's advice in comments (thanks!)
Since the value of an estimator is a function of the observed data, and the observed data is assumed to follow some distribution, it follows that the value of the estimator also follows some distribution. As the sample size gets large, estimators in the class of "M-estimators" become distributed according to a Normal distribution, and one can use this fact, along with a little bit of hope (or bootstrapping) to develop approximate confidence intervals.