Pick is the map algebra analog of a "case" or "switch" statement. Like them it is not indispensable but it can be convenient (and more efficient than deeply nested binary logical operators).
Notable among the uses to which I have put this operation is its ability to implement a cellular automaton.
Another handy use is random selection of rasters. A worked example appears on this site at Creating raster by randomly choosing cell value from multiple overlapping rasters?