There are times when it makes sense for multiple blockchains to be able to communicate. This is where Hyperledger Quilt comes in. Quilt is a tool that facilitates cross-Blockchain communication by implementing an Interledger protocol (ILP). The ILP is a generic specification available to all blockchains to allow cross-ledger communication, originally created by ripple labs. With ILP, two ledgers (they do not have to be blockchains) can coordinate, to exchange values from one ledger to the other.
ILP is a protocol that can be implemented using any programming language or technology, as long as it conforms to the standard. Because of this, it can be used to join multiple completely independent ledgers, even ones with radically different architecture. These ledgers do not need to be blockchains but can be any system of accounting. In ILP, cross-ledger communication occurs primarily through actors called connectors. See the following diagram from interledger.org:

The ILP bridges ledgers with a set of connectors. A connector is a system that provides the service of forwarding interledger communications towards their destination, similar to how packets are forwarded across the internet—peer to peer. ILP communication packets are sent from senders to a series of connectors that finally land at receivers.
The connectors are trusted participants in this sequence, and the sender and all intermediate connectors must explicitly trust one another. Unlike other blockchain-oriented technology, ILP does not involve trustless exchange. However, the sender and each connector need trust only their nearest links in the chain for it to work.
Quilt is the implementation of the ILP that has been donated to the Hyperledger project, on behalf of ripple labs, Everis, and NTT DATA. These organizations have also sponsored ongoing dedicated personnel to help improve the Quilt codebase, which is primarily in Java.