The JMP documentation is a little unclear--it just cites a book: Robust Regression and Outlier Detection.
However, it looks like the bracket contains the "highest density interval", or "highest probability density" interval. This is the smallest (i.e., shortest) interval that contains 50% of the data points.
Suppose your data looks like this
-30, -20, -10, 1, 2, 3, 4, 5, 6, 10, 20, 30.
The 50% densest region runs from 0 to 6 because it contains half the data (six of the twelve points) and is the shortest interval that does so (it's five units long;the next closest (2-10) is eight units long instead).
The highest probability interval often shows up in Bayesian settings, sometimes as an alternative to confidence intervals. Here, they probably mean for you to use it a heuristic for detecting outliers.