A discriminator tap allows you to decode certain data such as control channels for trunked systems. This is very useful. Even before trunk-tracking scanners were introduced, you could track Moto and EDACS systems using two receivers, a computer, and a "data slicer" (a simple interface into the computer), using FREE software. Audio from a control channel coming from the speaker is filtered and not suitable for decoding. The discriminator is further up the audio chain.
You can get lots of info about the system such as talkgroups, radio IDs, channels, and System IDs (for Moto systems). Some software like Trunker gives a real-time display of who's using which channels. Some multi-site systems even identify the site by name (GMCP Zone 2).
Dave