That appears to be from the SAS QUANTREG manual section:
They then go on to call the sparsity function. the "reciprocal of the density function" (which is arguably a natural language version of the formula above but is more suggestive that a local sparsity would be something like
1/(r_1-r_2) where r-1 and r_2 are local density residuals rather than just a functional "inverse".) So a natural interpretation is that the (local) sparsity function is very similar to the average distance between nearby ordered residuals. In fact this formula for empiric estimate of s() appears immediately below that description:
So the sparsity function is the local estimate of the average distance between nearby residuals on the original scale in the limit as "nearby" (defined by the bandwidth) gets small. I didn't really see how that matched up with what I knew about sandwich estimators, so I also looked at Koenker's quantreg R package where the mathematical definition appears:
> Hinv: inverse of the estimated Hessian matrix returned if cov=TRUE and
se != "iid".
> The Huber sandwich is cov = Hinv %*% J %*% Hinv.
Hinv matrices are what give the name "sandwich" to the method.
J is sandwiched between two