The Fediverse, short for federated universe, is a network of interconnected social media platforms and services that can communicate and interact with each other. Similar to email, where you can send emails to users with accounts on different services (like Gmail, Outlook, etc.), federation enables users to seamlessly connect with others across different social services.
The Fediverse allows the breaking down of walls between online communities and fosters a more open and interconnected experience. So, Flipboard users will be able to interact with a broader audience instead of only those with Flipboard accounts.