You could think of a network packet analyzer as a measuring device used to examine what's going on inside a network cable, just like a voltmeter is used by an electrician to examine what's going on inside an electric cable (but at a higher level, of course).
In the past, such tools were either very expensive, proprietary, or both. However, with the advent of Wireshark, all that has changed.
Wireshark is perhaps one of the best open source packet analyzers available today.
network administrators use it to troubleshoot network problems
network security engineers use it to examine security problems
developers use it to debug protocol implementations
people use it to learn network protocol internals