Stripe sells payments infrastructure for internet businesses: primarily, they help you bill your customers, process payments, and work with your payment data.
Accepting payments on the web is a pain in the ass that requires special bank accounts and working with companies with names like SecureNet and Authorize.Net (yikes)
Stripe gives developers a set of simple APIs for accepting and managing payments, and a web interface to explore and manage data manually
Stripe has expanded their product suite over time to include broader financial services and data products
In the developer world (and tech more broadly), Stripe is known as the gold standard for how to market to and build products for a technical (read: software engineer) audience. They’re also worth $36B, and are expanding into broader financial services.