A short version that leaves out a lot!
James Ide and I had a vague idea that mobile development was too hard and that someone should make it better, so we started researching the problem a few years ago.
I had managed the mobile teams at Quora but hadn't actually done much native mobile development myself. And James had mostly done web stuff at Facebook. So we experimented a lot with trying to make HTML5 perform really well and decided it wasn't going to work and then built an implementation of NodeJS for iOS on top of JavaScriptCore that would let you control native views from JS and we started to build stuff with that. One of our guiding ideas has always been that we want to make doing mobile development easier than web development.
When React Native native came out, we realized it was basically the exact same approach that we'd been taking but was a little further along. Since it was open source, we just decided to use it as the basis for everything else that we wanted to do. We built a very rough MVP of Exponent that we could show people and then we joined up with Brent, Jesse, and Nik. And later Ben, Skevy, and Adam and Jess to make it into something real.
And there is a great community of people who are interested in this stuff now that we've been able to collaborate with. Some of those people help make Exponent better like the team at Facebook who works on React Native (hi girls and guys!) and Janic and Satya and Tienson. And also developers who are making super cool stuff on Exponent. One of my favorite feelings is when I see something nifty that someone made with Exponent and our work feels like a part of making that happen.