Square added the ability to buy and sell Bitcoin through its Cash application. Cash is an application that allows you to instantly send and request money from friends. According to App Annie, Cash is the 30th most popular app in the Apple App Store. Even if the feature doesn't get much traction (which I doubt), this will bring more awareness (Streisand Effect) to the space. I don't expect much money to come into the market through the app, but I expect many people to purchase Bitcoin (or a part of one).
I had an interesting conversation on Twitter with @brooksmorgan. Brooks talked about if Square will require users to put in their Social Security #'s. All the US exchanges that handle fiat to cryptocurrencies such as Coinbase and Gemini put users through an extensive KYC/AML process. You do need to connect a credit card or bank account so Square might use that as part of the process. At the moment, Square doesn't allow you to send Bitcoin between users (arguably the primary use case of Bitcoin).
There really is a lot more questions than answers. How will Square be handling storage of the Bitcoin? What are the trading fees? Will they create a statement for taxes? But again, most users probably won't care. They have a trusted platform to buy Bitcoin and will be happy to use it. I expect we will continue to see large financial companies offer Bitcoin and other cryptocurrency products.