What does it mean when we say that the confidence interval methods of this section are robust against departures from normality?

Refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 “Airport Data Speeds” in Appendix B. The confidence level of 95% was used.

Data Set 32: Airport Data Speeds 

Data are from 50 airports (first five rows shown here) consisting of data speeds (Mbps) from four different cell phone carriers. Based on data from CNN.