I think Square organizes around how people gather and transact, and focus on the under-banked. They have good data to inform where that happens, in what quantities, and when. Clearly food places, craft fairs, and music festivals have been crucial marketplaces for them, and now they are establishing themselves as a promotional platform to those markets. They now have a lot of surfaces to do so, and will probably always now be after more ad inventory.
They are positioned to own not only how people transact in person, but who will be doing those transactions, where, and when.
Imagine they roll out a data product to their merchants that shows an Uber Hot-Spots style dataset of sales, demand, and trends in both merchandise and the wild psychographics you can learn from a music service.