Network validators, as part of their validating responsibilities, need to run this app along side the Parity node.
This app is responsible for calling the emitInitiateChange function on the Consensus contract.
The function is responsible for emitting the InitiateChange event described in Parity Wiki.
After this function is called successfully the validator set changes to a new one.
This app is also responsible for calling the emitRewardedOnCycle function on the BlockReward contract.
All the validators call those functions and only the first call is successful, but there's no loss of gas because they're called using a zero-gas transactions.
When running the quickstart script as valiadtor, this app is run automatically.
It can be started manually as well:
$ docker run --detach --name fuseapp --volume /home/fuse/fusenet/config:/config --restart=always fusenet/validator-app
Note that /home/fuse/fusenet/config is the folder where the key file and pass.pwd of the validator account should be placed. This is the default location for the quickstart script so there shouldn't be any problems there.