Basecamp's team struggled with spamming emails in their company. They had Highrise, a software for team communication and task-managing. They didn't have anything for "external" communication.
They started to work on Haystack. It was a prototype for work communication purposes, like contacting the press, receiving app notifications - everything that was a pain in the ass of the Basecamp's team members.
Haystack was built on the basis of Highrise. They tested it on their own conversations and threads. Later, they changed the project name to HEY, and continued to polish the app.
The founders tweeted a lot about HEY email. Both Jason Fried and David Heinemeier Hansson had quite powerful personal brands on Twitter, totaling of combined 640,000 followers, which they could capitalize on when promoting new email app. Since it fits perfectly what they'd been preaching before, many of their followers wanted to try it out.
Then they created an invite-only waitlist. A week since the app's launch, more than 100,000 people have already signed up.