What is the Monitor In/Thru on VoiceLive 3 for?
The Monitor In/Thru allows you to tie into a PA system and receive a "monitor" or "cue" mix from the main PA and hear it via your VoiceLive 3. With the Thru connection, you can seamlessly pass the signal on to any other monitors on stage too.
Using the independent headphone mix within VoiceLive 3, you can combine the incoming "monitor" mix with vocal, guitar and loop signals from your VoiceLive 3 to create a perfect monitor mix for yourself.
You might ask "But the monitor mix already has my VoiceLive 3 signal in it, since the rest of the band needs to hear me. What good does it do me to have it in the monitor mix AND the VoiceLive 3 itself"
Typically, most musicians in a band want to hear a nice mix of the whole group, with a bit "more me" in the signal. Since your monitor mix likely contains some of your vocal/guitar/loop signal from VoiceLive 3, the internal headphone mix allows you to blend that signal relative to the existing vocal, guitar and loop signals, giving you exactly the mix you want.
It might sound a bit confusing, but you'll see that it's quite easy in practice.