This video investigates discrete-time signal differencing and summation
The discrete-time signal y[k] = x[k]-x[k-1] is the difference of adjacent time samples of the x[k]. This discrete-time operation is analogous to taking the derivative of a continuous-time signal. This operation is a high-pass operation since adjacent samples that are close in amplitude have a small difference (i.e. low-frequency terms are rejected) while adjacent samples that are different in amplitude have a large difference (i.e. high-frequency terms are amplified).
The discrete-time signal y[k] = sum x[m] for m = -infinity to k is the summation of the signal x[k]. At any time k, the signal y[k] is the cumulative sum of all previous values of x[k]. This discrete-time operaiton is analogous to taking the integral of a continuous-time signal. This operation is a low-pass operation since high-frequency changes in the signal x[k] are "smoothed out" by the summation operation.