Put simply, an Underscore music mix is a version of the
song where all the lead-instruments have been taken out. What's left is the
basic backbone groove of the track.
Underscore versions are often very well suited for media presentations because
the music provides an "atmosphere", but it doesn't stick it's head
out and demand attention. This ensures that the actual message you're trying
to get across isn't diluted or disturbed by any element in the music.
But Underscore versions are sometimes suitable for other things as well.
Some people simply prefer the Underscore version. When you remove the lead
instruments, you are left with a different perspective on the real back bone
of the music. It can cast a whole new light on the composition.
Generally, unless otherwise stated, the Underscore version has the same length
as the Full Length version.