It could offer a viable alternative to Visa/Mastercard for large merchants during negotiations (such as Costco).
For cardholders, it could improve Capital One's ability to offer cashback and other benefits, since now they own the payment network (and won't have to pay fees to Visa/Mastercard). For example, Discover bank has been able to offer 1% cash back on their debit card.
C1 plans to significantly expand Discover's acceptance internationally. That is a benefit to consumers. However, it will take some time, and in the interim, it could limit C1's cards internationally. Their travel cards will hopefully stay on Visa/Mastercard until they get the international network in place.
Of course Capital One will try to maximize their profits, but I could see some minimal benefit to merchants and consumers.