Connext is a payments API for Ethereum developers. Currently, users have to go through an incredibly high friction process (including creating a virtual currency exchange account which can take 3+ days) in order to buy the app-tokens required to use Ethereum applications. Oftentimes, these decentralized apps are cheaper, better and more ethically designed than their centralized competitors but struggle to gain traction with non-technical consumers because of the difficulty of their use.
With Connext, Ethereum developers can sell their app-tokens directly to users with credit cards using a Stripe-like API. This opens up an entirely new market for these applications and brings the technology into the mainstream market.