Interledger came out of our work on Codius - basically we wanted a way that you could pay smart contract hosts. But we thought that different hosts would want to accept different currencies, so we didn't just want to integrate with one cryptocurrency or another. We wanted a solution where the host (i.e. merchant) could accept whatever they wanted and the user could pay with whatever they wanted.

Interledger is a protocol that does that. The merchant and the user have to agree on a cryptographic primitive (e.g. SHA256) and their ledgers have to support escrow based on that primitive (Bitcoin does) and then they can transact safely via connectors that anyone can run and that are completely untrusted.