Multiplexers have many uses. They route signals according to an input address. They can be used to pass on only signals of interest. This can be useful to cut down on the number of channels you need. For example, suppose you have lots of signals you want to digitize or process. But most of the time the lines are quiet. It's expensive to build processing electronics for every single channel. Let's say you have 100 signal lines, but at any given time only one is active. You can use a multiplexer to select only the active line to pass on for processing, and thereby save money by building only one channel of electronics for processing instead of 100.
Multiplexers can also be used to turn parallel data into serial data, i.e., to change a set of bits presented in parallel to a set of bits sent one at a time. Eggleston discusses this application in Section 8.15.