Yeah, I forgot to consider how some characters benefit more from certain badges than others...
Anyway, unlike a traditional air dash where the your character travels a fixed distance before you are allowed to attack, air dash break allows characters to attack at any point in the air dash and cause them to fall immediately as soon as they attack.
I'm not sure if my description is clear enough so here is a video of Novriltataki explaining the airdash break mechanic using footage from the previous GGST beta.
The above example is only for the forward version from GGST but Chaos Code allowed it to be used in both directions so it was used a lot in neutral and mixups and I really like it as I think the mechanic is really cool but it's also really strong so don't feel obligated to include it if you think that it'll be too strong.