Federation here means accessing the entities of one Wikibase Repository from another Wikibase Repository.

“Foreign” is used to mean that something refers to and comes from another Wikibase repository.
Foreign EntityIds and mappings are documented in the file docs/foreign-entity-ids.wiki in the wikibase/data-model component.

As of March 2017:

In order to enable access to entities from federated repositories both Repo and Client components must be enabled.
Accessing data of foreign entities relies on the shared database access (databases of federated repositories must be in the same database cluster).

2020 will add API (instead of DB) based federation as described above (one entity source per entity type).

Configuration

A Wikibase Repository is configured as documented in Options.
In order for federation to work foreign sources must be configured using the entitySources setting.

To see an example please look at the dedicated entitysources topic.