This Wired article provides a great overview of why Stripe has been so successful at getting folks like Lyft, Instacart and other tech start-ups to push billions of dollars of transactions through it's pipes.
The young co-founders of Stripe, brothers Patrick and John Collison, began the company in 2009 as a project to make accepting credit cards easier but soon saw a grander opportunity in building a better interface for the messy systems that power the digital transfer of money—a black box that makes enabling online transactions as easy as embedding a photo or video in a blog post. Stripe’s pitch is that it has created a kind of shorthand that lets coders access and leverage all the power of that infrastructure without having to learn its entire lexicon.
http://www.wired.com/2014/07/the-startup-that-wants-to-change-the-language-of-online-payments/