Standard linear filtering on data acts "separately" in each direction: along rows, columns (and time, depth or wavelength for 3D data, like video, tomography or multispectral images). If you look at a given 2D filter (applies to 3D too) in each direction $d$, you can feel the nature of the filter.
If the coeficients sum to one, then a constant signal turns into a constant signal of the same amplitude. Constant signal are low frequency, so by continuity, you expect a low-pass behavior. If the coeficients sum to zero, then a constant signal turns to zero, so you can image a low-cut behavior.
If the sum of coefficients with alternating signs ($c_1,c_2,\ldots,c_n \to -c_1,c_2,\ldots,(-1)^n c_n$) is one, then you can expect a high-pass behavior. If they sum to zero, then a high-cut effect is plausible.
One can interpret this as integrating in one direction, differentiating in the other. You can also look at the sums not only in the horizontal and vertical directions, but along diagonal or other slopes.
So keeping with linearfilters, many useful filters in ipmage processing either:
1. sum to 1 in both directions (and often sum to a small value with alternating signs): they are mostly blurring kernels
2. sum to 1 in one direction, to 0 in the other: they are directional filters, detecting edges along the $0$-sum direction
Some filters like the Lapcian sum to zeros by combining both directions.