As an example, Air Canada operates its own brand for international flights, but has a subsidiary called Air Canada Rouge for domestic and US flights. What's the reason for creating such subsidiaries?
Sometimes it can be for the purpose of recruiting pilots and cabin crew at lower pay. The airline may have pay agreements, possibly union collective agreements or else just formal agreements with non-union "associations", which set pay, working hours, and other conditions. This can be a barrier to offering ultra-low-cost tickets on the discount brand. If they structure the low-cost brand as a nominally separate entity, those agreements won't extend to it. See, for example, this news story on Westjet's new low-cost brand.
But there are lots of other brand-management reasons they might do this. They may want the big brand associated with reliable, high-service business travel for which they can charge full fare; and the new brand associated with cheap fares at the expense of everything else. Look at how the car companies spawn different brands so they can focus their marketing on luxury (Infiniti) mass-market (Toyota) and fun-and-cheap (Scion, now rolled into Toyota).