What does the term robust statistics mean?

It means that a test or technique is relatively insensitive to violations of its statistical assumptions. In particular, it refers to the degree to which a parametric technique can be used on data whose distribution departs from normality and still gives results that are close to what they would be if the data were normally distributed.

Robustness in statistics can have two meanings. Robustness against outliers and robustness agist parametric assumptions.