Standard linear filtering on regularly-sampled data acts "separately" in each cartesian 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 coefficients sum to one, then a constant input signal turns into a constant output signal of the same amplitude. Constant signal are low frequency, so by continuity, you expect a low-pass behavior. If the coefficients sum to zero, then a constant signal turns to zero, so you can imagine a low-cut behavior.
In a dual manner, 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 linear filters, many useful filters in image processing either:
- Sum to 1 in both directions (and often sum to a small value with alternating signs): they are mostly blurring kernels
- 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 Laplacian mask, sum to zeros by combining both directions.