An "indulgent buy" is buying something that you normally wouldn't because it is too expensive, or you don't really need it (for example, you have so many bags already... you don't need another!)
"This bag is truly an indulgent buy because I wouldn't normally buy something so expensive!"
"This bag is truly an indulgent buy because I have worked hard lately and deserve a reward or treat!"
"This bag is truly an indulgent buy because I have so many bags at home and don't really need another, but I can't pass this one up!"
To "indulge" means to allow personal enjoyment of something that gives you pleasure, in this case the pleasure is buying the bag (but for some it can mean having a drink; or eating something they would not normally allow themselves, like a big piece of chocolate cake!)