The more elaborate tra jacks are used in half normal and full normal patching situations.
Think patchbays. Say you have a row of patch points that have you mic inputs of a console on them. Below them are you mic tie lines from your live room/ISO booths. If the patch bay is setup correctly, ideally that mic signal will flow directly to that console input with nothing patched in. Without getting to deep, it can also be setup for breaking that connection on the sending or receiving side.
Say, an external mic pre output is normaled to a console input(output goes to input without a patch cable inserted. Let's say channel one. Usually you'll set it up where one can insert a cable at the pre output point and sent it somewhere else. Say a compressor. That line level signal is now split at that patch point, going both to channel one and the compressor. You can patch the compressor in on channel 2. Now you have compressed signal and uncompressed signal on adjacent channels. Move the compressed cable to channel one patch point and it breaks the signal split at the patchbay and only the compressed signal is present.
This is a very useful way to setup as it saves manual patches(less spaghetti) and allows you to do things like split signals without using the busses of the console.