MSD is a measure of the displacement over a certain interval of time, used for instance to analyze trajectories and tell if it's ballistic, diffusive, sub-diffusive, etc.
To compute MSD, all the possible time intervals within the trajectory need to be considerer. The simplest way uses nested loops :
the first loop runs over the time points, the other loop runs over the possible interval from each time point.
Thoses nested loops are a nightmare for fast computation, especially for long trajectories.
Kehl suppresses the loops, and computes all the squared distance at once, then sorts and averages them out.
A mispelling in a comment