A relay is a piece of software that increases federation between instances that subscribe to that relay.
It is a great way for smaller instances to populate their federated timeline.

How to subscribe to a relay

Only instance admins can subscribe to a relay. In Mastodon you can do that by going to Settings > Administration > Relays. There you can enter the url of the relay - add "/inbox" at the end of it.
Then you just have to wait for your instance to be accepted by the relay owners.

List of ready to use Fediverse relays

Comparison of Fediverse relay software

relay name source works with
diaspora* Mastodon Misskey Pleroma
Activity relay https://github.com/yukimochi/Activity-Relay ✖️ ✔️ ✔️ ✖️
ActivityRelay https://git.pleroma.social/pleroma/relay ✖️ ✔️ ✔️ ✔️
Pub relay https://source.joinmastodon.org/mastodon/pub-relay ✖️ ✔️ ✔️ ✔️
Seattle relay https://gitlab.com/jankysolutions/social.seattle.wa.us/relay ✖️ ✔️ ✔️ ✔️
Social relay https://github.com/jaywink/social-relay ✔️ ✖️ ✖️ ✖️
AodeRelay https://git.asonix.dog/asonix/relay ✖️ ✔️ ✔️ ✔️

You can find usage statistics of relay software from The Federation for activityrelay, activity-relay, aoderelay, pub-relay, selective-relay, unicarelay.

How to install your own Fediverse relay for beginners

To be written.