From the Mother manual:
"Most instrument amps have an inherent/baked-in voicing that emphasizes treble, bass, and cuts mids to varying degrees (Yes, even amps that are typically referred to as “mid-heavy”). This EQ curve compliments guitar and bass pickups, and for better or worse, is what we’re accustomed to hearing as a “neutral” or even “natural” electric guitar sound. The Mother preamp pedal replicates the full tonal response of the real amp (with a flattering EQ curve of its own), but what happens when you take that carefully designed EQ curve and run it into the frontend of a typical guitar or bass amp? Essentially, two EQ's in a row. Double the bass, double the mid-scoop, and double the treble. Too much of a good thing by most standards, creating an exaggerated EQ curve that for most situations would be undesirable (this is subjective, of course). To solve this, the Mother's leftmost jack, simply-named Output, is carefully voiced to work with your amps existing preamp, so it won't get too boomy, scooped, or harsh, while keeping full functionality of the pedal's EQ controls."
So, the Output jack has some high and low dialed back to better match going into the from of an amp rig. To get their fully flavored amp simulation, you use the Direct Out jack. I guess it sort of like the Origin Bassrig mini bass and treble controls on their 1/4" out, intended to contour the Bassrig for plugging into the front of an amp.