The main use case of the Arbitrary Message Bridge (AMB) between the Rinkeby Testnet and the xDai chain is to relay tokens emitted by Reddit (e.g. Moons and Bricks) to a chain with real value (xDai) through the AMB extensions.
DApp developers may also find this pair of chains useful for their cross-chain applications. In order to organize cross-chain communication, applications can implement their own AMB extension. This is represented by two mediator contracts so that either assets or arbitrary data can be transferred between chains. The deployed mediator contracts do not require a set of oracles to be setup, providing the main functionality to end users immediately, without needing to spend resources on setting up the entire infrastructure.