"Mg" is short for "Mega". Many generations ago, Yamaha introduced the "Mega" concept which was a way to produce more realistic sounds leveraging arpeggio playback.

It's easy to explain what "Mega" is by giving an acoustic guitar example.

When you're playing acoustic guitar, sometimes you slide your fretting hand which creates a high-pitched "swipe!" sound. Adding this sound to acoustic guitar would enhance the sound. Sometimes when playing, your hand may hit the body of the guitar and produce a "thud" sound. Having this sound, at the right time, would enhance the sound. When playing with a pick, you hear the pick noise on up and down strokes. Having this noise would enhance the sound.

Lets say we have an acoustic guitar sound with the lowest key on your keyboard as the "thud", the next key up as the pick sound, and next key up as the "swipe!" sound. If you were to play this manually, you'd have to do lots of keyboard gymnastics in order to play the lowest 3 notes at the exact right time to make a convincing pick/thud/swipe sound to make for a more realistic acoustic guitar.

This is where "Mega" comes in. It plays those added extras at the exact correct time because the arpeggio is programmed to handle this for you.

You could try to do this manually - and no doubt there are players out there who have achieved some form of mastery of being able to add different elements to their direct playing of instruments so they can get close to a "Mega" arpeggio without having to use one. I personally do not use arpeggios during live play and opt for non-mega sounds so that I can control the tempo/pattern/etc in real-time. It's not as realistic if you were to solo my keyboard-guitar work apart from everything else. However, it's not under that kind of scrutiny live - it's behind many other things. So it's fine. If you were producing a track where you have more control over everything - a Mega arpeggio may be the way to go.

Mega Arps depend on the extra "noises" to be in very specific MIDI notes of the Part that Arp was designed for. Mega Arps therefore cannot be transferred to different (random) sounds unless those other Parts have the same noises in the same locations. Not all bass sounds, for example, have these. Those basses will sound strange when playing with a Mega Arp - because those basses may have standard bass notes instead of finger noises or swipe noises or glissando down or other effects that the Arp is intending to play.

https://www.yamahasynth.com/ask-a-question/montage-same-arp-types-and-arp-engine-as-motif

MODX Reference Manual (pdf) page 12