Juggling is when you hit the opponent while they're in a state of falling. The purpose of this is to extend combos. It can be to inflict max damage, carry your opponent to the corner, force a hard knockdown, or to cause a "reset situation" (forcing P2 to land on their feet). In mugen, juggling is decided by how many points you have after hitting with a move that causes knockdown. If any following attack requires more points than you have, you will be unable to start or continue the juggle combo.
In the constants, airjuggle is the number of points you start with.
life = 1000
power = 5000
attack = 100
defence = 100
airjuggle = 15 ;<-----you start with 15 points
To assign the number of points to a move, add juggle to the StateDef.
type = S
movetype = A
physics = N
anim = 200
velset = 0,0
ctrl = 0
juggle = 5 ;<-----this move takes 5 points
Points can also be assigned to the HitDef. Mainly used for for projectiles.
[State 200, HitDef]
type = HitDef
trigger1 = AnimElemTime(3) >= 0 && AnimElemTime(4) < 0
attr = S,NA
air.juggle = 2 ;<-----this move takes 2 points
Finally, AssertSpecial can be used to bypass the juggle system entirely by using NoJuggleCheck.
To note: Mugen's juggle system has it's limits, and you'll notice that a number of creators have made their own juggle system instead. If you're editing someone's character, do not be surprised if anything mentioned here doesn't work.