Instead of making an account on one site (reddit) and only being able to use that account on the one site, you can create an account on one instance, and then participate on every other instance that is federated with your instance. Logging in using one account between otherwise isolated websites is federation.
instances: can also be called servers, anyone can host a lemmy code.
community: synonym for subreddit
federation: instances can federate (connect) to each other and their users can interact with the connected instances, they can also defederate (disconnect).